<PAGE>

                                                                    Exhibit 10.8


THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER
THE SECURITIES ACT OF 1933, AS AMENDED, OR APPLICABLE STATE SECURITIES LAWS.
THE SECURITIES HAVE BEEN ACQUIRED FOR INVESTMENT AND MAY NOT BE OFFERED FOR
SALE, SOLD, TRANSFERRED OR ASSIGNED (1) IN THE ABSENCE OF AN EFFECTIVE
REGISTRATION STATEMENT FOR THE SECURITIES UNDER THE SECURITIES ACT OF 1933, AS
AMENDED (THE "1933 ACT"), OR APPLICABLE STATE SECURITIES LAWS, OR (2) IN THE
ABSENCE OF AN OPINION OF COUNSEL, IN A GENERALLY ACCEPTABLE FORM, THAT
REGISTRATION IS NOT REQUIRED UNDER THE 1933 ACT OR (3) UNLESS SOLD, TRANSFERRED
OR ASSIGNED PURSUANT TO RULE 144 UNDER SAID ACT.


                                DATA RACE, INC.

                         Common Stock Purchase Warrant

Warrant No.:   2001A-1                             Number of Shares: 583,333
Date of Issuance:  May 11, 2001


Data Race Inc., a Texas corporation doing business as IP Axess (the "Company"),
                                                                     -------
hereby certifies that, for Ten United States Dollars ($10.00) and other good and
valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, First Capital Group of Texas II, L.P., the registered holder
hereof or its permitted assigns, is entitled, subject to the terms set forth
below, to purchase from the Company upon surrender of this Warrant, at any time
or times on or after the date hereof, but not after 11:59 P.M. Central Time on
the Expiration Date (as defined herein) Five Hundred Eighty-Three Thousand Three
Hundred Thirty-Three (583,333) fully paid nonassessable shares of Common Stock
(as defined herein) (the "Warrant Shares") at the purchase price per share
                          --------------
provided in Section 1(b) below.

     Section 1.

          (a) Securities Purchase Agreement.  This Warrant certificate
              -----------------------------
represents one of the Common Stock Purchase Warrants issued pursuant to the
terms of that certain Securities Purchase Agreement dated as of May 11, 2001,
among the Company and the Buyers referred to therein (the "Securities Purchase
                                                           -------------------
Agreement").
---------

          (b) Definitions.  The following words and terms as used in this
              -----------
Warrant shall have the following meanings:

              (i) "Common Stock" means (i) the Company's common stock, no par
                   ------------
value per share, and (ii) any capital stock into which such Common Stock shall
have been changed or any capital stock resulting from a reclassification of such
Common Stock.

                                       1
<PAGE>

          (ii)   "Common Stock Deemed Outstanding" means, at any given time, the
                  -------------------------------
number of shares of Common Stock actually outstanding at such time, plus the
number of shares of Common Stock deemed to be outstanding pursuant to Sections
8(b)(i) and 8(b)(ii) hereof regardless of whether the Options (as defined below)
or Convertible Securities (as defined below) are actually exercisable or
convertible at such time, but excluding any shares of Common Stock owned or held
by or for the account of the Company or issuable upon exercise of the Common
Stock Purchase Warrants issued pursuant to the Securities Purchase Agreement.

          (iii)  "Convertible Securities" means any stock or securities (other
                  ----------------------
than Options) directly or indirectly convertible into or exchangeable for Common
Stock.

          (iv)   "Exempt Issuance" means (A) a loan from a commercial bank which
                  ---------------
has only an incidental equity feature or any equity line or similar transaction
from any financial institution, (B) any transaction involving the Company's
issuances of securities (1) as consideration in a merger or consolidation, (2)
in connection with a strategic partnership or joint venture (the primary purpose
of which is not to raise equity capital), or (3) as consideration for the
acquisition of a business, product, license or other assets by the Company, (C)
the issuance of common stock in a firm commitment, underwritten public offering,
(D) the issuance of securities upon exercise or conversion of the Company's
options, warrants or other convertible securities outstanding as of the date
hereof, (E) the grant of additional options or warrants, or the issuance of
additional securities, under any Company stock option plan, restricted stock
plan,  stock purchase plan or other plan or written compensation agreement for
the benefit of the Company's employees, directors, consultants or advisors, or
(F) the issuance of securities pursuant to any shareholder rights plan adopted
by the Company prior to the Closing (as defined in the Securities Purchase
Agreement).

          (v)    "Expiration Date" means the date five (5) years from the date
                  ---------------
of this Warrant or, if such date falls on a Saturday, Sunday or other day on
which banks are required or authorized to be closed in the City of Dallas or the
State of Texas or on which trading does not take place on the principal exchange
or automated quotation system on which the Common Stock is traded (a "Holiday"),
the next date that is not a Holiday.

          (vi)   "Fair Market Value" means as of any specified date, the closing
                  -----------------
price of the Common Stock on the NASDAQ National Market (or, if the Common Stock
is not listed thereon, such other national securities exchange on which the
Common Stock is then listed) on that date, or if no prices are reported on that
date, on the last preceding date on which such prices of the Common Stock are so
reported.  If the Common Stock is not then listed on any national securities
exchange but is traded over the counter at the time the determination of the
Fair Market Value of the Common Stock is required to be made hereunder, such
Fair Market Value shall be deemed to be equal to the average between the
reported high and low sales prices of the Common Stock on the most recent date
on which the Common Stock was publicly traded. If the Common Stock is not
publicly traded at the time the determination of the Fair Market Value thereof
is required to be made hereunder, the determination of such Fair Market Value
shall be made by the Board of Directors of the Company in good faith.

                                       2
<PAGE>

              (vii)   "Options" means any rights, warrants or options to
                       -------
subscribe for or purchase Common Stock or Convertible Securities.

              (viii)  "Other Securities" means (i) the Common Stock Purchase
                       ----------------
Warrants issued pursuant to the Securities Purchase Agreement, not including
this Warrant and (ii) the Company's 10% Secured Convertible Promissory Notes
issued pursuant to the Securities Purchase Agreement.

              (ix)    "Person" means an individual, a limited liability company,
                       ------
a partnership, a joint venture, a corporation, a trust, an unincorporated
organization and a government or any department or agency thereof.

              (x)     "Securities Act" means the Securities Act of 1933, as
                       --------------
amended.

              (xi)    "Warrant" means this Warrant and all Warrants issued in
                       -------
exchange, transfer or replacement of any thereof.

              (xii)   "Warrant Exercise Price" shall be $0.30 per common share,
                       ----------------------
subject to adjustment as hereinafter provided.

  Section 2.  Exercise of Warrant.
              -------------------

          (a) Subject to the terms and conditions hereof, this Warrant may be
exercised by the holder hereof then registered on the books of the Company, in
whole or in part, at any time on any Business Day (as defined in the Securities
Purchase Agreement) on or after the opening of business on the date hereof and
prior to 11:59 P.M. Central Time on the Expiration Date by (i) delivery of a
written notice, in the form of the subscription notice attached as Exhibit A
                                                                   ---------
hereto (the "Exercise Notice"), of such holder's election to exercise this
             ---------------
Warrant, which notice shall specify the number of Warrant Shares to be
purchased, (ii) payment to the Company of an amount equal to the Warrant
Exercise Price multiplied by the number of Warrant Shares as to which this
Warrant is being exercised (plus any applicable issue or transfer taxes) (the

"Aggregate Exercise Price") (x) in cash or by check or wire transfer, (y) in
 ------------------------
unissued Warrant Shares then issuable upon exercise of this Warrant and
surrendered to the Company for cancellation, or (z) in a combination thereof,
and (iii) the surrender to a common carrier for delivery to the Company as soon
as practicable following such date, this Warrant (or an indemnification
undertaking with respect to this Warrant in the case of its loss, theft or
destruction); provided, that if such Warrant Shares are to be issued in any name
other than that of the registered holder of this Warrant, such issuance shall be
deemed a transfer and the provisions of Section 7 shall be applicable.  For
purposes of determining the amount, if any, of the Aggregate Exercise Price
satisfied by the payment in unissued Warrant Shares surrendered to the Company
for cancellation, each such surrendered Warrant Share shall be valued at an
amount equal to the Fair Market Value of a share of the Common Stock of the
Company less the Warrant Exercise Price of such surrendered Warrant Share.  In
the event of any exercise of the rights represented by this Warrant in
compliance with this Section 2(a), a certificate or certificates for the Warrant
Shares so purchased, in such denominations as may be requested by the holder
hereof and registered in the name of, or as directed by, the holder, shall be
delivered at the

                                       3
<PAGE>

Company's expense to, or as directed by, such holder as soon as practicable, and
in no event later than two Business Days, after the Company's receipt of the
Exercise Notice, the Aggregate Exercise Price and this Warrant (or an
indemnification undertaking with respect to this Warrant in the case of its
loss, theft or destruction). Upon delivery of the Exercise Notice and Aggregate
Exercise Price referred to in clause (ii) above, the holder of this Warrant
shall be deemed for all corporate purposes to have become the holder of record
of the Warrant Shares with respect to which this Warrant has been exercised,
irrespective of the date of delivery of this Warrant as required by clause (iii)
above or the certificates evidencing such Warrant Shares.

          (b) Unless the rights represented by this Warrant shall have expired
or shall have been fully exercised, the Company shall, as soon as practicable
and in no event later than five (5) Business Days after any exercise and at its
own expense, issue a new Warrant identical in all respects to this Warrant
exercised except it shall represent rights to purchase the number of Warrant
Shares purchasable immediately prior to such exercise under this Warrant
exercised, less the number of Warrant Shares with respect to which such Warrant
is exercised.

          (c) No fractional shares of Common Stock are to be issued upon the
exercise of this Warrant, but rather the number of shares of Common Stock issued
upon exercise of this Warrant shall be rounded up or down to the nearest whole
number.

          (d) If the Company shall fail for any reason or for no reason to issue
to the holder on a timely basis as described in this Section 2, a certificate
for the number of shares of Common Stock to which the holder is entitled upon
the holder's exercise of this Warrant or a new Warrant for the number of shares
of Common Stock to which such holder is entitled pursuant to Section 2(b)
hereof, the Company shall, in addition to any other remedies under this Warrant
or the Securities Purchase Agreement or otherwise available to such holder,
including any indemnification under the Securities Purchase Agreement, pay as
additional damages in cash to such holder on each day the issuance of such
Common Stock certificate or new Warrant, as the case may be, is not timely
effected an amount equal to 0.25% of the product of (A) the sum of the number of
shares of Common Stock not issued to the holder on a timely basis and to which
the holder is entitled and/or, the number of shares represented by the portion
of this Warrant which is not being converted, as the case may be, and (B) the
average of the closing bid price of the Common Stock for the three consecutive
trading days immediately preceding the last possible date which the Company
could have issued such Common Stock or Warrant, as the case may be, to the
holder without violating this Section 2.


  Section 3.  Covenants as to Common Stock.  The Company hereby covenants and
              ----------------------------
agrees as follows:

          (a) This Warrant is, and any Warrant issued in substitution for or
replacement of this Warrant will upon issuance be, duly authorized and validly
issued.

          (b) All Warrant Shares which may be issued upon the exercise of the
rights represented by this Warrant will, upon issuance, be validly issued, fully
paid and nonassessable and free from all taxes, liens and charges with respect
to the issue thereof.

                                       4
<PAGE>

          (c) During the period within which the rights represented by this
Warrant may be exercised, the Company will at all times have authorized and
reserved at least 100% of the number of shares of Common Stock needed to provide
for the exercise of the rights then represented by this Warrant and the par
value, if any, of said shares will at all times be less than or equal to the
applicable Warrant Exercise Price.

          (d) The Company shall promptly secure the listing of the shares of
Common Stock issuable upon exercise of this Warrant upon each national
securities exchange or automated quotation system, if any, upon which shares of
Common Stock are then listed (subject to official notice of issuance upon
exercise of this Warrant) and shall maintain, so long as any other shares of
Common Stock shall be so listed, such listing of all Warrant Shares from time to
time issuable upon the exercise of this Warrant; and the Company shall so list
on each national securities exchange or automated quotation system, as the case
may be, and shall maintain such listing of any other shares of capital stock of
the Company issuable upon the exercise of this Warrant if and so long as any
shares of the same class shall be listed on such national securities exchange or
automated quotation system.

          (e) The Company will not, by amendment of its Articles of
Incorporation or through any reorganization, transfer of assets, consolidation,
merger, dissolution, issue or sale of securities, or any other voluntary action,
avoid or seek to avoid the observance or performance of any of the terms to be
observed or performed by it hereunder, but will at all times in good faith
assist in the carrying out of all the provisions of this Warrant and in the
taking of all such action as may reasonably be requested by the holder of this
Warrant in order to protect the exercise privilege of the holder of this Warrant
against dilution or other impairment, consistent with the tenor and purpose of
this Warrant will take all such actions as may be necessary or appropriate in
order that the Company may validly and legally issue fully paid and
nonassessable shares of Common Stock upon the exercise of this Warrant.

  Section 4.  Taxes.  The Company shall pay any and all taxes which may be
              -----
payable with respect to the issuance and delivery of Warrant Shares upon
exercise of this Warrant.

  Section 5.  Warrant Holder Not Deemed a Stockholder.  Except as otherwise
              ---------------------------------------
specifically provided herein, no holder, as such, of this Warrant shall be
entitled to vote or receive dividends or be deemed the holder of shares of the
Company for any purpose, nor shall anything contained in this Warrant be
construed to confer upon the holder hereof, as such, any of the rights of a
stockholder of the Company or any right to vote, give or withhold consent to any
corporate action (whether any reorganization, issue of stock, reclassification
of stock, consolidation, merger, conveyance or otherwise), receive notice of
meetings, receive dividends or subscription rights, or otherwise, prior to the
issuance to the holder of this Warrant of the Warrant Shares which he or she is
then entitled to receive upon the due exercise of this Warrant.  In addition,
nothing contained in this Warrant shall be construed as imposing any liabilities
on such holder to purchase any securities (upon exercise of this Warrant or
otherwise) or as a stockholder of the Company, whether such liabilities are
asserted by the Company or by creditors of the Company.  Notwithstanding this
Section 5, the Company will provide the holder

                                       5
<PAGE>

of this Warrant with copies of the same notices and other information given to
the shareholders of the Company generally, contemporaneously with the giving
thereof to the shareholders.

     Section 6.  [Omitted]

     Section 7.  Ownership and Transfer.
                 ----------------------

             (a) The Company shall maintain at its principal executive offices
(or such other office or agency of the Company as it may designate by notice to
the holder hereof), a register for this Warrant, in which the Company shall
record the name and address of the person in whose name this Warrant has been
issued, as well as the name and address of each transferee. The Company may
treat the person in whose name any Warrant is registered on the register as the
owner and holder thereof for all purposes, notwithstanding any notice to the
contrary, but in all events recognizing any transfers made in accordance with
the terms of this Warrant.

             (b) This Warrant and the rights granted to the holder hereof are
transferable, in whole or in part, upon surrender of this Warrant, together with
a properly executed warrant power in the form of Exhibit B attached hereto;
provided, however, that any transfer or assignment shall be subject to the
conditions set forth in Section 7(c) below.

             (c) The holder of this Warrant understands that this Warrant has
not been and is not expected to be, registered under the Securities Act or any
state securities laws, and may not be offered for sale, sold, assigned or
transferred unless (a) subsequently registered thereunder, or (b) such holder
shall have delivered to the Company an opinion of counsel, in generally
acceptable form, to the effect that the securities to be sold, assigned or
transferred may be sold, assigned or transferred pursuant to an exemption from
such registration; provided that (i) any sale of such securities made in
reliance on Rule 144 promulgated under the Securities Act may be made only in
accordance with the terms of said Rule and further, if said Rule is not
applicable, any resale of such securities under circumstances in which the
seller (or the person through whom the sale is made) may be deemed to be an
underwriter (as that term is defined in the Securities Act) may require
compliance with some other exemption under the Securities Act or the rules and
regulations of the Securities and Exchange Commission thereunder; and (ii)
neither the Company nor any other person is under any obligation to register the
Warrants under the Securities Act or any state securities laws or to comply with
the terms and conditions of any exemption thereunder.

             (d) The Company is obligated to register the Warrant Shares for
resale under the Securities Act pursuant to the Registration Rights Agreement
dated May 11, 2001 by and between the Company and the Buyers listed on the
signature page thereto (the "Registration Rights Agreement") and the initial
                             -----------------------------
holder of this Warrant (and certain assignees thereof) is entitled to the
registration rights in respect of the Warrant Shares as set forth in the
Registration Rights Agreement.

                                       6
<PAGE>

  Section 8.  Adjustment of Warrant Exercise Price and Number of Shares.  The
              ---------------------------------------------------------
Warrant Exercise Price and the number of shares of Common Stock issuable upon
exercise of this Warrant shall be adjusted from time to time as follows:

          (a) Adjustment of Warrant Exercise Price and Number of Shares upon
              --------------------------------------------------------------
Issuance of Common Stock.  If and whenever on or after the date of issuance of
------------------------
this Warrant, the Company issues or sells, or in accordance with Section 8(b) is
deemed to have issued or sold, any shares of Common Stock (including the
issuance or sale of shares of Common Stock owned or held by or for the account
of the Company, but excluding shares of Common Stock deemed to have been issued
by the Company in connection with an Exempt Issuance or upon exercise or
conversion of the Other Securities) for consideration per share (the "Applicable
                                                                      ----------
Price") which is less than the Warrant Exercise Price in effect immediately
-----
prior to such time, then immediately after such issue or sale the Warrant
Exercise Price then in effect shall be reduced to an amount equal to the
Applicable Price.  Upon each such adjustment of the Warrant Exercise Price
hereunder, the number of Warrant Shares acquirable upon exercise of this Warrant
shall be adjusted to the number of shares determined by dividing (i) the product
of (x) the Warrant Exercise Price in effect immediately prior to such adjustment
and (y) the number of shares of Warrant Shares acquirable upon exercise of this
Warrant immediately prior to such adjustment by (ii) the Warrant Exercise Price
resulting from such adjustment.

          (b) Effect on Warrant Exercise Price of Certain Events.  For purposes
              --------------------------------------------------
of determining the adjusted Warrant Exercise Price under Section 8(a) above, the
following shall be applicable:

              (i)  Issuance of Options.  If the Company in any manner grants any
                   -------------------
Options and the lowest price per share for which one share of Common Stock is
issuable upon the exercise of any such Option or upon conversion or exchange of
any Convertible Securities issuable upon exercise of any such Option is less
than the Warrant Exercise Price then in effect, then such share of Common Stock
shall be deemed to be outstanding and to have been issued and sold by the
Company at the time of the granting or sale of such Option for such price per
share.  For purposes of this Section 8(b)(i), the "lowest price per share for
which one share of Common Stock is issuable upon exercise of such Options or
upon conversion or exchange of such Convertible Securities" shall be equal to
the sum of the lowest amounts of consideration (if any) received or receivable
by the Company with respect to any one share of Common Stock upon the granting
or sale of the Option, upon exercise of the Option and upon conversion or
exchange of any Convertible Security issuable upon exercise of such Option. No
further adjustment of the Warrant Exercise Price shall be made upon the actual
issuance of such Common Stock or of such Convertible Securities upon the
exercise of such Options or upon the actual issuance of such Common Stock upon
conversion or exchange of such Convertible Securities.  Notwithstanding the
foregoing, no adjustment shall be made pursuant to this Section 8(b)(i) to the
extent that such adjustment is based solely on the fact that the Convertible
Securities issuable upon exercise of such Option are convertible into or
exchangeable for Common Stock at a price which varies with the market price of
the Common Stock.

              (ii) Issuance of Convertible Securities.  If the Company in any
                   ----------------------------------
manner issues or sells any Convertible Securities and the lowest price per share
for which one share of

                                       7
<PAGE>

Common Stock is issuable upon such conversion or exchange thereof is less than
the Warrant Exercise Price then in effect, then such share of Common Stock shall
be deemed to be outstanding and to have been issued and sold by the Company at
the time of the issuance or sale of such Convertible Securities for such price
per share. For the purposes of this Section 8(b)(ii), the "lowest price per
share for which one share of Common Stock is issuable upon such conversion or
exchange" shall be equal to the sum of the lowest amounts of consideration (if
any) received or receivable by the Company with respect to one share of Common
Stock upon the issuance or sale of the Convertible Security and upon conversion
or exchange of such Convertible Security. No further adjustment of the Warrant
Exercise Price shall be made upon the actual issuance of such Common Stock upon
conversion or exchange of such Convertible Securities, and if any such issue or
sale of such Convertible Securities is made upon exercise of any Options for
which adjustment of the Warrant Exercise Price had been or are to be made
pursuant to other provisions of this Section 8(b), no further adjustment of the
Warrant Exercise Price shall be made by reason of such issue or sale.
Notwithstanding the foregoing, no adjustment shall be made pursuant to this
Section 8(b)(ii) to the extent that such adjustment is based solely on the fact
that such Convertible Securities are convertible into or exchangeable for Common
Stock at a price which varies with the market price of the Common Stock.

          (iii)  Change in Option Price or Rate of Conversion.  If the purchase
                 --------------------------------------------
price provided for in any Options, the additional consideration, if any, payable
upon the issue, conversion or exchange of any Convertible Securities, or the
rate at which any Convertible Securities are convertible into or exchangeable
for Common Stock changes at any time, the Warrant Exercise Price in effect at
the time of such change shall be adjusted to the Warrant Exercise Price which
would have been in effect at such time had such Options or Convertible
Securities provided for such changed purchase price, additional consideration or
changed conversion rate, as the case may be, at the time initially granted,
issued or sold and the number of shares of Common Stock acquirable hereunder
shall be correspondingly readjusted.  For purposes of this Section 8(b)(iii), if
the terms of any Option or Convertible Security that was outstanding as of the
date of issuance of this Warrant are changed in the manner described in the
immediately preceding sentence, then such Option or Convertible Security and the
Common Stock deemed issuable upon exercise, conversion or exchange thereof shall
be deemed to have been issued as of the date of such change.  No adjustment
shall be made if such adjustment would result in an increase of the Warrant
Exercise Price then in effect.

          (iv)   Treatment of Expired Options and Unexercised Convertible
                 --------------------------------------------------------
Securities.  If, in any case, the total number of shares of Common Stock
----------
issuable upon the exercise of any Option or upon exercise, conversion or
exchange of any Convertible Security is not, in fact, issued and the rights to
exercise such Option or to exercise, convert or exchange such Convertible
Securities shall have expired or terminated, the Warrant Exercise Price then in
effect will be readjusted to the Warrant Exercise Price which would have been in
effect at the time of such expiration or termination had such Option or
Convertible Securities, to the extent outstanding immediately prior to such
expiration or termination (other than in respect of the actual number of shares
of Common Stock issued upon exercise or conversion thereof) never been issued.

                                       8
<PAGE>

          (c) Effect on Warrant Exercise Price of Certain Events.  For purposes
              --------------------------------------------------
of determining the adjusted Warrant Exercise Price under Sections 8(a) and 8(b),
the following shall be applicable:

              (i)  Calculation of Consideration Received.  In case any Option is
                   -------------------------------------
issued in connection with the issue or sale of other securities of the Company,
together comprising one integrated transaction in which no specific
consideration is allocated to such Options by the parties thereto, the Options
will be deemed to have been issued for a consideration of $.01.  If any Common
Stock, Options or Convertible Securities are issued or sold or deemed to have
been issued or sold for cash, the consideration received therefor will be deemed
to be the amount received by the Company therefor before deduction of reasonable
commissions, underwriting discounts or allowances or other similar reasonable
expenses incurred by the Company.  If any Common Stock, Options or Convertible
Securities are issued or sold for a consideration other than cash, the amount of
such consideration received by the Company will be the fair value of such
consideration, except where such consideration consists of securities that are
listed for trading on a national securities exchange or automated quotation
system, in which case the amount of consideration received by the Company will
be the average market price of such securities for the twenty (20) consecutive
trading days immediately preceding the date of receipt.  If any Common Stock,
Options or Convertible Securities are issued to the owners of the non-surviving
entity in connection with any merger in which the Company is the surviving
entity, the amount of consideration therefor will be deemed to be the fair value
of such portion of the net assets and business of the non-surviving entity as is
attributable to such Common Stock, Options or Convertible Securities, as the
case may be.  The fair value of any consideration other than cash or securities
that are listed for trading on a national securities exchange or automated
quotation system will be determined jointly by the Company and the holders of
Warrants representing a majority of the shares of Common Stock obtainable upon
exercise of the Warrants then outstanding.  If such parties are unable to reach
agreement within ten (10) days after the occurrence of an event requiring
valuation (the "Valuation Event"), the fair value of such consideration will be
                ---------------
determined within five Business Days after the tenth (10th) day following the
Valuation Event by an independent, reputable appraiser jointly selected by the
Company and the holders of Warrants representing two-thirds majority of the
shares of Common Stock obtainable upon exercise of the Warrants then
outstanding.  The determination of such appraiser shall be final and binding
upon all parties and the fees and expenses of such appraiser shall be borne by
the Company.

              (ii) Record Date.  If the Company takes a record of the holders of
                   -----------
Common Stock for the purpose of entitling them (1) to receive a dividend or
other distribution payable in Common Stock, Options or in Convertible Securities
or (2) to subscribe for or purchase Common Stock, Options or Convertible
Securities, then such record date will be deemed to be the date of the issue or
sale of the shares of Common Stock deemed to have been issued or sold upon the
declaration of such dividend or the making of such other distribution or the
date of the granting of such right of subscription or purchase, as the case may
be.

          (d) Adjustment of Warrant Exercise Price upon Subdivision or
              --------------------------------------------------------
Combination of Common Stock.  If the Company at any time after the date of
---------------------------
issuance of this Warrant subdivides (by any stock split, stock dividend,
recapitalization or otherwise) one or more classes

                                       9
<PAGE>

of its outstanding shares of Common Stock into a greater number of shares, the
Warrant Exercise Price in effect immediately prior to such subdivision will be
proportionately reduced and the number of shares of Common Stock obtainable upon
exercise of this Warrant will be proportionately increased. If the Company at
any time after the date of issuance of this Warrant combines (by combination,
reverse stock split or otherwise) one or more classes of its outstanding shares
of Common Stock into a smaller number of shares, the Warrant Exercise Price in
effect immediately prior to such combination will be proportionately increased
and the number of shares of Common Stock obtainable upon exercise of this
Warrant will be proportionately decreased.

          (e) Distribution of Assets.  If the Company shall declare or make any
              ----------------------
distribution of its assets (or rights to acquire its assets) to holders of
Common Stock as a partial liquidating dividend, by way of return of capital or
otherwise (including, without limitation, any distribution of cash, property or
securities of a subsidiary) (a "Distribution"), at any time after the issuance
                                ------------
of this Warrant, then, in each such case:

              (i)  the Warrant Exercise Price in effect immediately prior to the
close of business on the record date fixed for the determination of holders of
Common Stock entitled to receive the Distribution shall be reduced, effective as
of the close of business on such record date, to a price determined by
multiplying such Warrant Exercise Price by a fraction of which (A) the numerator
shall be the closing bid price on the trading day immediately preceding such
record date minus the value of the Distribution (as determined in good faith by
the Company's Board of Directors) applicable to one share of Common Stock, and
(B) the denominator shall be the closing bid price on the trading day
immediately preceding such record date; and

              (ii) either (A) the number of Warrant Shares obtainable upon
exercise of this Warrant shall be increased to a number of shares equal to the
number of shares of Common Stock obtainable immediately prior to the close of
business on the record date fixed for the determination of holders of Common
Stock entitled to receive the Distribution multiplied by the reciprocal of the
fraction set forth in the immediately preceding clause (i), or (B) in the event
that the Distribution is of common stock of a company whose common stock is
traded on a national securities exchange or a national automated quotation
system, then the holder of this Warrant shall receive an additional warrant to
purchase Common Stock, the terms of which shall be identical to those of this
Warrant, except that such warrant shall be exercisable into the amount of the
assets that would have been payable to the holder of this Warrant pursuant to
the Distribution had the holder exercised this Warrant immediately prior to such
record date and with an exercise price equal to the amount by which the exercise
price of this Warrant was decreased with respect to the Distribution pursuant to
the terms of the immediately preceding clause (i).

          (f) Certain Events.  If any event occurs of the type contemplated by
              --------------
the provisions of this Section 8 but not expressly provided for by such
provisions (including, without limitation, the granting of stock appreciation
rights, phantom stock rights or other rights with equity features), then the
Company's Board of Directors will make an appropriate adjustment in the Warrant
Exercise Price and the number of Warrant Shares obtainable upon exercise of this
Warrant so as to protect the rights of the holders of the Warrants; provided
that no such

                                       10
<PAGE>

adjustment will increase the Warrant Exercise Price or decrease the number of
shares of Common Stock obtainable as otherwise determined pursuant to this
Section 8.

          (g)  Notices.
               -------

              (i)   Immediately upon any adjustment of the Warrant Exercise
Price, the Company will give written notice thereof to the holder of this
Warrant, setting forth in reasonable detail, and certifying, the calculation of
such adjustment.

              (ii)  The Company will give written notice to the holder of this
Warrant at least twenty (20) days prior to the date on which the Company closes
its books or takes a record (A) with respect to any dividend or distribution
upon the Common Stock, (B) with respect to any pro rata subscription offer to
holders of Common Stock or (C) for determining rights to vote with respect to
any Organic Change (as defined below), dissolution or liquidation, provided that
such information shall be made known to the public prior to or in conjunction
with such notice being provided to such holder.

              (iii) The Company will also give written notice to the holder of
this Warrant at least twenty (20) days prior to the date on which any Organic
Change (as defined below), dissolution or liquidation will take place, provided
that such information shall be made known to the public prior to or in
conjunction with such notice being provided to such holder.

  Section 9.  Purchase Rights; Reorganization, Reclassification,
                 --------------------------------------------------
Consolidation, Merger or Sale.
-----------------------------
          (a) If at any time after the date hereof, the Company grants, issues
or sells any Options, Convertible Securities or rights to purchase stock,
warrants, securities or other property pro rata to the record holders of any
class of Common Stock (the "Purchase Rights"), then the holder of this Warrant
                            ---------------
will be entitled to acquire, upon the terms applicable to such Purchase Rights,
the aggregate Purchase Rights which such holder could have acquired if such
holder had held the number of shares of Common Stock acquirable upon complete
exercise of this Warrant immediately before the date on which a record is taken
for the grant, issuance or sale of such Purchase Rights, or, if no such record
is taken, the date as of which the record holders of Common Stock are to be
determined for the grant, issue or sale of such Purchase Rights.

          (b) Any recapitalization, reorganization, reclassification,
consolidation, merger, sale of all or substantially all of the Company's assets
to another Person or other transaction which is effected in such a way that
holders of Common Stock are entitled to receive (either directly or upon
subsequent liquidation) stock, securities or assets with respect to or in
exchange for Common Stock is referred to herein as "Organic Change."  Prior to
                                                    --------------
the consummation of any (i) sale of all or substantially all of the Company's
assets to an acquiring Person or (ii) other Organic Change following which the
Company is not a surviving entity, the Company will use its best efforts to
secure from the Person purchasing such assets or the successor resulting from
such Organic Change (in each case, the "Acquiring Entity") written agreement (in
                                        ----------------
form and substance satisfactory to the holders of Warrants representing a
majority of the shares of Common Stock obtainable upon exercise of the Warrants
then outstanding) to

                                       11
<PAGE>

deliver to each holder of Warrants in exchange for such Warrants, a security of
the Acquiring Entity evidenced by a written instrument substantially similar in
form and substance to this Warrant and satisfactory to the holders of the
Warrants (including, an adjusted warrant exercise price equal to the value for
the Common Stock reflected by the terms of such consolidation, merger or sale,
and exercisable for a corresponding number of shares of Common Stock acquirable
and receivable upon exercise of the Warrants, if the value so reflected is less
than the Warrant Exercise Price in effect immediately prior to such
consolidation, merger or sale). Prior to the consummation of any other Organic
Change, the Company shall use its best efforts to make appropriate provision (in
form and substance satisfactory to the holders of Warrants representing a
majority of the shares of Common Stock obtainable upon exercise of the Warrants
then outstanding) to ensure that each of the holders of the Warrants will
thereafter have the right to acquire and receive in lieu of or in addition to
(as the case may be) the Warrant Shares immediately theretofore acquirable and
receivable upon the exercise of such holder's Warrants, such shares of stock,
securities or assets that would have been issued or payable in such Organic
Change with respect to or in exchange for the number of Warrant Shares which
would have been acquirable and receivable upon the exercise of such holder's
Warrant as of the date of such Organic Change (without taking into account any
limitations or restrictions on the exercisability of this Warrant).

          (c) In the event the Company proposes to effect an Organic Change,
then in addition to any other rights the holder may have, the holder shall have
the right to effect a Cashless Exercise (as defined below), by presentation and
surrender of this Warrant to the Company at its principal executive offices with
a written notice of the holder's intention to effect a Cashless Exercise,
including a calculation of the number of shares of Common Stock to be issued
upon such exercise in accordance with the terms hereof.  A "Cashless Exercise"
                                                            -----------------
shall mean that, in lieu of paying the Warrant Exercise Price in cash, the
holder shall surrender this Warrant for that number of Warrant Shares determined
by subtracting from the number of Warrant Shares otherwise issuable to the
holder upon such exercise, an amount of Warrant Shares (the "Surrendered
                                                             -----------
Shares") having a closing bid price (as reported by Bloomberg) on the date
------
immediately preceding the date of the exercise notice equal to the Aggregate
Exercise Price (as defined in Section 2) of the Warrant Shares for which this
Warrant is being exercised; and thereafter the Surrendered Shares shall no
longer be available for issuance hereunder.

  Section 10. Lost, Stolen, Mutilated or Destroyed Warrant.  If this Warrant
              --------------------------------------------
is lost, stolen, mutilated or destroyed, the Company shall, on receipt of an
indemnification undertaking, issue a new Warrant of like denomination and tenor
as this Warrant so lost, stolen, mutilated or destroyed.

  Section 11. Notice.  Any notices, consents, waivers or other communications
              ------
required or permitted to be given under the terms of this Warrant must be in
writing and will be deemed to have been delivered: (i) upon receipt, when
delivered personally; (ii) upon receipt, when sent by facsimile (provided
confirmation of transmission is mechanically or electronically generated and
kept on file by the sending party); or (iii) one Business Day after deposit with
a nationally recognized overnight delivery service, in each case properly
addressed to the party to receive the same. The addresses and facsimile numbers
for such communications shall be:

                                       12
<PAGE>

          If to the Company:

               Data Race Inc.
               6509 Windcrest Drive, Suite 120
               Plano, Texas 75024
               Telephone:    (972) 205-4005
               Facsimile:    (210) 558-0356
               Attention:    James G. Scogin

          With copy to:

               Jackson Walker LLP
               901 Main Street, Suite 6000
               Dallas, Texas 75202
               Telephone:    (214) 953 - 5801
               Facsimile:    (214) 953 - 5736
               Attention:    James S. Ryan, III, Esq.

If to a holder of this Warrant, to it at the address and facsimile number set
forth on the Schedule of Buyers to the Securities Purchase Agreement, with
copies to such holder's representatives as set forth on such Schedule of Buyers,
or at such other address and facsimile as shall be delivered to the Company upon
the issuance or transfer of this Warrant.  Each party shall provide five days'
prior written notice to the other party of any change in address or facsimile
number.  Written confirmation of receipt (A) given by the recipient of such
notice, consent, waiver or other communication, (B) mechanically or
electronically generated by the sender's facsimile machine containing the time,
date, recipient facsimile number and an image of the first page of such
transmission or (C) provided by a nationally recognized overnight delivery
service shall be rebuttable evidence of personal service, receipt by facsimile
or receipt from a nationally recognized overnight delivery service in accordance
with clause (i), (ii) or (iii) above, respectively.

     Section 12.  [Omitted]

     Section 13.  Date.  The date of this Warrant is May 11, 2001.  This
                  ----
Warrant, in all events, shall be wholly void and of no effect after the close of
business on the Expiration Date, except that notwithstanding any other
provisions hereof, the provisions of Section 7 shall continue in full force and
effect after such date as to any Warrant Shares or other securities issued upon
the exercise of this Warrant.

     Section 14.  Amendment and Waiver.  Except as otherwise provided herein,
                  --------------------
the provisions of the Warrants may be amended and the Company may take any
action herein prohibited, or omit to perform any act herein required to be
performed by it, only if the Company has obtained the written consent of the
holders of Warrants representing two-thirds of the shares of Common Stock
obtainable upon exercise of the Warrants then outstanding; provided that no such
action may increase the Warrant Exercise Price of the Warrants or decrease the
number of

                                       13
<PAGE>

shares or class of stock obtainable upon exercise of any Warrants without the
written consent of the holder of such Warrant.

     Section 15.  Descriptive Headings; Governing Law.  The descriptive headings
                  -----------------------------------
of the several Sections and paragraphs of this Warrant are inserted for
convenience only and do not constitute a part of this Warrant.  This Warrant
shall be governed by the internal laws of the State of Texas, without giving
effect to any choice of law or conflict of law provision or rule (whether of the
State of Texas or any other jurisdictions) that would cause the application of
the laws of any jurisdictions other than the State of Texas.


                           [Signature Page Follows]

                                       14
<PAGE>

     This Warrant has been duly executed by the Company as of the date first set
forth above.


                                    DATA RACE INC.


                                    By:
                                         ------------------------------------
                                    Name:  James G. Scogin
                                         ------------------------------------
                                    Title:  Senior Vice President, Chief
                                            Financial Officer


                                       15
<PAGE>

                             EXHIBIT A TO WARRANT
                             --------------------

                               SUBSCRIPTION FORM

       TO BE EXECUTED BY THE REGISTERED HOLDER TO EXERCISE THIS WARRANT

                                DATA RACE INC.

     The undersigned holder hereby exercises the right to purchase ___________
of the shares of Common Stock ("Warrant Shares") of Data Race Inc., a Texas
corporation (the "Company"), evidenced by the attached Warrant (the "Warrant").
Capitalized terms used herein and not otherwise defined shall have the
respective meanings set forth in the Warrant.

     1.  Payment of Warrant Exercise Price.  The holder shall pay the sum of
$___________________ to the Company in accordance with the terms of the Warrant.

     2.  Delivery of Warrant Shares.  The Company shall deliver to the holder
__________ Warrant Shares in accordance with the terms of the Warrant.



Date:                        ,
      ----------------- ----   -------




Name of Registered Holder


By:
    -----------------------------------
Name:
     ----------------------------------
Title:
      ---------------------------------

                                       16
<PAGE>

                              EXHIBIT B TO WARRANT
                              --------------------

                             FORM OF WARRANT POWER


FOR VALUE RECEIVED, the undersigned does hereby assign and transfer to
________________, Federal Identification No. __________, a warrant to purchase
____________ shares of the capital stock of Data Race Inc., a Texas corporation,
represented by warrant certificate no. _____, standing in the name of the
undersigned on the books of said corporation.  The undersigned does hereby
irrevocably constitute and appoint ______________, attorney to transfer the
warrants of said corporation, with full power of substitution in the premises.


Dated:  _________, 200__






                              ---------------------------------------------

                              By:
                                  -----------------------------------------
                              Name:
                                   ----------------------------------------
                              Title:
                                    ---------------------------------------

                                       17
<PAGE>

                                                                    Exhibit 10.8

THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER
THE SECURITIES ACT OF 1933, AS AMENDED, OR APPLICABLE STATE SECURITIES LAWS.
THE SECURITIES HAVE BEEN ACQUIRED FOR INVESTMENT AND MAY NOT BE OFFERED FOR
SALE, SOLD, TRANSFERRED OR ASSIGNED (1) IN THE ABSENCE OF AN EFFECTIVE
REGISTRATION STATEMENT FOR THE SECURITIES UNDER THE SECURITIES ACT OF 1933, AS
AMENDED (THE "1933 ACT"), OR APPLICABLE STATE SECURITIES LAWS, OR (2) IN THE
ABSENCE OF AN OPINION OF COUNSEL, IN A GENERALLY ACCEPTABLE FORM, THAT
REGISTRATION IS NOT REQUIRED UNDER THE 1933 ACT OR (3) UNLESS SOLD, TRANSFERRED
OR ASSIGNED PURSUANT TO RULE 144 UNDER SAID ACT.


                                DATA RACE, INC.

                         Common Stock Purchase Warrant

Warrant No.:   2001A-2                        Number of Shares:  833,333
Date of Issuance:  May 11, 2001


Data Race Inc., a Texas corporation doing business as IP Axess (the "Company"),
                                                                     -------
hereby certifies that, for Ten United States Dollars ($10.00) and other good and
valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, ICN Capital Ltd., the registered holder hereof or its permitted
assigns, is entitled, subject to the terms set forth below, to purchase from the
Company upon surrender of this Warrant, at any time or times on or after the
date hereof, but not after 11:59 P.M. Central Time on the Expiration Date (as
defined herein) Eight Hundred Thirty-Three Thousand Three Hundred Thirty-Three
(833,333) fully paid nonassessable shares of Common Stock (as defined herein)
(the "Warrant Shares") at the purchase price per share provided in Section 1(b)
      --------------
below.

     Section 1.

          (a) Securities Purchase Agreement.  This Warrant certificate
              -----------------------------
represents one of the Common Stock Purchase Warrants issued pursuant to the
terms of that certain Securities Purchase Agreement dated as of May 11, 2001,
among the Company and the Buyers referred to therein (the "Securities Purchase
                                                           -------------------
Agreement").
---------

          (b) Definitions.  The following words and terms as used in this
              -----------
Warrant shall have the following meanings:

              (i) "Common Stock" means (i) the Company's common stock, no par
                   ------------
value per share, and (ii) any capital stock into which such Common Stock shall
have been changed or any capital stock resulting from a reclassification of such
Common Stock.

                                       1
<PAGE>

          (ii) "Common Stock Deemed Outstanding" means, at any given time, the
                -------------------------------
number of shares of Common Stock actually outstanding at such time, plus the
number of shares of Common Stock deemed to be outstanding pursuant to Sections
8(b)(i) and 8(b)(ii) hereof regardless of whether the Options (as defined below)
or Convertible Securities (as defined below) are actually exercisable or
convertible at such time, but excluding any shares of Common Stock owned or held
by or for the account of the Company or issuable upon exercise of the Common
Stock Purchase Warrants issued pursuant to the Securities Purchase Agreement.

          (iii)  "Convertible Securities" means any stock or securities (other
                  ----------------------
than Options) directly or indirectly convertible into or exchangeable for Common
Stock.

          (iv) "Exempt Issuance" means (A) a loan from a commercial bank which
                ---------------
has only an incidental equity feature or any equity line or similar transaction
from any financial institution, (B) any transaction involving the Company's
issuances of securities (1) as consideration in a merger or consolidation, (2)
in connection with a strategic partnership or joint venture (the primary purpose
of which is not to raise equity capital), or (3) as consideration for the
acquisition of a business, product, license or other assets by the Company, (C)
the issuance of common stock in a firm commitment, underwritten public offering,
(D) the issuance of securities upon exercise or conversion of the Company's
options, warrants or other convertible securities outstanding as of the date
hereof, (E) the grant of additional options or warrants, or the issuance of
additional securities, under any Company stock option plan, restricted stock
plan,  stock purchase plan or other plan or written compensation agreement for
the benefit of the Company's employees, directors, consultants or advisors, or
(F) the issuance of securities pursuant to any shareholder rights plan adopted
by the Company prior to the Closing (as defined in the Securities Purchase
Agreement).

          (v) "Expiration Date" means the date five (5) years from the date of
               ---------------
this Warrant or, if such date falls on a Saturday, Sunday or other day on which
banks are required or authorized to be closed in the City of Dallas or the State
of Texas or on which trading does not take place on the principal exchange or
automated quotation system on which the Common Stock is traded (a "Holiday"),
the next date that is not a Holiday.

          (vi) "Fair Market Value" means as of any specified date, the closing
                -----------------
price of the Common Stock on the NASDAQ National Market (or, if the Common Stock
is not listed thereon, such other national securities exchange on which the
Common Stock is then listed) on that date, or if no prices are reported on that
date, on the last preceding date on which such prices of the Common Stock are so
reported.  If the Common Stock is not then listed on any national securities
exchange but is traded over the counter at the time the determination of the
Fair Market Value of the Common Stock is required to be made hereunder, such
Fair Market Value shall be deemed to be equal to the average between the
reported high and low sales prices of the Common Stock on the most recent date
on which the Common Stock was publicly traded. If the Common Stock is not
publicly traded at the time the determination of the Fair Market Value thereof
is required to be made hereunder, the determination of such Fair Market Value
shall be made by the Board of Directors of the Company in good faith.

                                       2
<PAGE>

                 (vii)  "Options" means any rights, warrants or options to
                         -------
subscribe for or purchase Common Stock or Convertible Securities.

                 (viii)  "Other Securities" means (i) the Common Stock Purchase
                          ----------------
Warrants issued pursuant to the Securities Purchase Agreement, not including
this Warrant and (ii) the Company's 10% Secured Convertible Promissory Notes
issued pursuant to the Securities Purchase Agreement.

                 (ix) "Person" means an individual, a limited liability
                       ------
company, a partnership, a joint venture, a corporation, a trust, an
unincorporated organization and a government or any department or agency
thereof.

                 (x) "Securities Act" means the Securities Act of 1933, as
                      --------------
amended.

                 (xi) "Warrant" means this Warrant and all Warrants issued in
                       -------
exchange, transfer or replacement of any thereof.

                 (xii)  "Warrant Exercise Price" shall be $0.30 per common
                         ----------------------
share, subject to adjustment as hereinafter provided.

     Section 2.  Exercise of Warrant.
                 -------------------

          (a) Subject to the terms and conditions hereof, this Warrant may be
exercised by the holder hereof then registered on the books of the Company, in
whole or in part, at any time on any Business Day (as defined in the Securities
Purchase Agreement) on or after the opening of business on the date hereof and
prior to 11:59 P.M. Central Time on the Expiration Date by (i) delivery of a
written notice, in the form of the subscription notice attached as Exhibit A
                                                                   ---------
hereto (the "Exercise Notice"), of such holder's election to exercise this
             ---------------
Warrant, which notice shall specify the number of Warrant Shares to be
purchased, (ii) payment to the Company of an amount equal to the Warrant
Exercise Price multiplied by the number of Warrant Shares as to which this
Warrant is being exercised (plus any applicable issue or transfer taxes) (the
"Aggregate Exercise Price") (x) in cash or by check or wire transfer, (y) in
-------------------------
unissued Warrant Shares then issuable upon exercise of this Warrant and
surrendered to the Company for cancellation, or (z) in a combination thereof,
and (iii) the surrender to a common carrier for delivery to the Company as soon
as practicable following such date, this Warrant (or an indemnification
undertaking with respect to this Warrant in the case of its loss, theft or
destruction); provided, that if such Warrant Shares are to be issued in any name
other than that of the registered holder of this Warrant, such issuance shall be
deemed a transfer and the provisions of Section 7 shall be applicable.  For
purposes of determining the amount, if any, of the Aggregate Exercise Price
satisfied by the payment in unissued Warrant Shares surrendered to the Company
for cancellation, each such surrendered Warrant Share shall be valued at an
amount equal to the Fair Market Value of a share of the Common Stock of the
Company less the Warrant Exercise Price of such surrendered Warrant Share.  In
the event of any exercise of the rights represented by this Warrant in
compliance with this Section 2(a), a certificate or certificates for the Warrant
Shares so purchased, in such denominations as may be requested by the holder
hereof and registered in the name of, or as directed by, the holder, shall be
delivered at the

                                       3
<PAGE>

Company's expense to, or as directed by, such holder as soon as practicable, and
in no event later than two Business Days, after the Company's receipt of the
Exercise Notice, the Aggregate Exercise Price and this Warrant (or an
indemnification undertaking with respect to this Warrant in the case of its
loss, theft or destruction). Upon delivery of the Exercise Notice and Aggregate
Exercise Price referred to in clause (ii) above, the holder of this Warrant
shall be deemed for all corporate purposes to have become the holder of record
of the Warrant Shares with respect to which this Warrant has been exercised,
irrespective of the date of delivery of this Warrant as required by clause (iii)
above or the certificates evidencing such Warrant Shares.

          (b) Unless the rights represented by this Warrant shall have expired
or shall have been fully exercised, the Company shall, as soon as practicable
and in no event later than five (5) Business Days after any exercise and at its
own expense, issue a new Warrant identical in all respects to this Warrant
exercised except it shall represent rights to purchase the number of Warrant
Shares purchasable immediately prior to such exercise under this Warrant
exercised, less the number of Warrant Shares with respect to which such Warrant
is exercised.

          (c) No fractional shares of Common Stock are to be issued upon the
exercise of this Warrant, but rather the number of shares of Common Stock issued
upon exercise of this Warrant shall be rounded up or down to the nearest whole
number.

          (d) If the Company shall fail for any reason or for no reason to issue
to the holder on a timely basis as described in this Section 2, a certificate
for the number of shares of Common Stock to which the holder is entitled upon
the holder's exercise of this Warrant or a new Warrant for the number of shares
of Common Stock to which such holder is entitled pursuant to Section 2(b)
hereof, the Company shall, in addition to any other remedies under this Warrant
or the Securities Purchase Agreement or otherwise available to such holder,
including any indemnification under the Securities Purchase Agreement, pay as
additional damages in cash to such holder on each day the issuance of such
Common Stock certificate or new Warrant, as the case may be, is not timely
effected an amount equal to 0.25% of the product of (A) the sum of the number of
shares of Common Stock not issued to the holder on a timely basis and to which
the holder is entitled and/or, the number of shares represented by the portion
of this Warrant which is not being converted, as the case may be, and (B) the
average of the closing bid price of the Common Stock for the three consecutive
trading days immediately preceding the last possible date which the Company
could have issued such Common Stock or Warrant, as the case may be, to the
holder without violating this Section 2.


     Section 3.  Covenants as to Common Stock.  The Company hereby covenants and
                 ----------------------------
agrees as follows:

          (a) This Warrant is, and any Warrant issued in substitution for or
replacement of this Warrant will upon issuance be, duly authorized and validly
issued.

          (b) All Warrant Shares which may be issued upon the exercise of the
rights represented by this Warrant will, upon issuance, be validly issued, fully
paid and nonassessable and free from all taxes, liens and charges with respect
to the issue thereof.


                                      4
<PAGE>

          (c) During the period within which the rights represented by this
Warrant may be exercised, the Company will at all times have authorized and
reserved at least 100% of the number of shares of Common Stock needed to provide
for the exercise of the rights then represented by this Warrant and the par
value, if any, of said shares will at all times be less than or equal to the
applicable Warrant Exercise Price.

          (d) The Company shall promptly secure the listing of the shares of
Common Stock issuable upon exercise of this Warrant upon each national
securities exchange or automated quotation system, if any, upon which shares of
Common Stock are then listed (subject to official notice of issuance upon
exercise of this Warrant) and shall maintain, so long as any other shares of
Common Stock shall be so listed, such listing of all Warrant Shares from time to
time issuable upon the exercise of this Warrant; and the Company shall so list
on each national securities exchange or automated quotation system, as the case
may be, and shall maintain such listing of any other shares of capital stock of
the Company issuable upon the exercise of this Warrant if and so long as any
shares of the same class shall be listed on such national securities exchange or
automated quotation system.

          (e) The Company will not, by amendment of its Articles of
Incorporation or through any reorganization, transfer of assets, consolidation,
merger, dissolution, issue or sale of securities, or any other voluntary action,
avoid or seek to avoid the observance or performance of any of the terms to be
observed or performed by it hereunder, but will at all times in good faith
assist in the carrying out of all the provisions of this Warrant and in the
taking of all such action as may reasonably be requested by the holder of this
Warrant in order to protect the exercise privilege of the holder of this Warrant
against dilution or other impairment, consistent with the tenor and purpose of
this Warrant will take all such actions as may be necessary or appropriate in
order that the Company may validly and legally issue fully paid and
nonassessable shares of Common Stock upon the exercise of this Warrant.

     Section 4.  Taxes.  The Company shall pay any and all taxes which may be
                 -----
payable with respect to the issuance and delivery of Warrant Shares upon
exercise of this Warrant.

     Section 5.  Warrant Holder Not Deemed a Stockholder.  Except as otherwise
                 ---------------------------------------
specifically provided herein, no holder, as such, of this Warrant shall be
entitled to vote or receive dividends or be deemed the holder of shares of the
Company for any purpose, nor shall anything contained in this Warrant be
construed to confer upon the holder hereof, as such, any of the rights of a
stockholder of the Company or any right to vote, give or withhold consent to any
corporate action (whether any reorganization, issue of stock, reclassification
of stock, consolidation, merger, conveyance or otherwise), receive notice of
meetings, receive dividends or subscription rights, or otherwise, prior to the
issuance to the holder of this Warrant of the Warrant Shares which he or she is
then entitled to receive upon the due exercise of this Warrant.  In addition,
nothing contained in this Warrant shall be construed as imposing any liabilities
on such holder to purchase any securities (upon exercise of this Warrant or
otherwise) or as a stockholder of the Company, whether such liabilities are
asserted by the Company or by creditors of the Company.  Notwithstanding this
Section 5, the Company will provide the holder


                                      5
<PAGE>

of this Warrant with copies of the same notices and other information given to
the shareholders of the Company generally, contemporaneously with the giving
thereof to the shareholders.

     Section 6.  [Omitted]

     Section 7.  Ownership and Transfer.
                 ----------------------

          (a) The Company shall maintain at its principal executive offices (or
such other office or agency of the Company as it may designate by notice to the
holder hereof), a register for this Warrant, in which the Company shall record
the name and address of the person in whose name this Warrant has been issued,
as well as the name and address of each transferee.  The Company may treat the
person in whose name any Warrant is registered on the register as the owner and
holder thereof for all purposes, notwithstanding any notice to the contrary, but
in all events recognizing any transfers made in accordance with the terms of
this Warrant.

          (b) This Warrant and the rights granted to the holder hereof are
transferable, in whole or in part, upon surrender of this Warrant, together with
a properly executed warrant power in the form of Exhibit B attached hereto;
provided, however, that any transfer or assignment shall be subject to the
conditions set forth in Section 7(c) below.

          (c) The holder of this Warrant understands that this Warrant has not
been and is not expected to be, registered under the Securities Act or any state
securities laws, and may not be offered for sale, sold, assigned or transferred
unless (a) subsequently registered thereunder, or (b) such holder shall have
delivered to the Company an opinion of counsel, in generally acceptable form, to
the effect that the securities to be sold, assigned or transferred may be sold,
assigned or transferred pursuant to an exemption from such registration;
provided that (i) any sale of such securities made in reliance on Rule 144
promulgated under the Securities Act may be made only in accordance with the
terms of said Rule and further, if said Rule is not applicable, any resale of
such securities under circumstances in which the seller (or the person through
whom the sale is made) may be deemed to be an underwriter (as that term is
defined in the Securities Act) may require compliance with some other exemption
under the Securities Act or the rules and regulations of the Securities and
Exchange Commission thereunder; and (ii) neither the Company nor any other
person is under any obligation to register the Warrants under the Securities Act
or any state securities laws or to comply with the terms and conditions of any
exemption thereunder.

          (d) The Company is obligated to register the Warrant Shares for resale
under the Securities Act pursuant to the Registration Rights Agreement dated May
11, 2001 by and between the Company and the Buyers listed on the signature page
thereto (the "Registration Rights Agreement") and the initial holder of this
              -----------------------------
Warrant (and certain assignees thereof) is entitled to the registration rights
in respect of the Warrant Shares as set forth in the Registration Rights
Agreement.

                                       6
<PAGE>

     Section 8.  Adjustment of Warrant Exercise Price and Number of Shares.  The
                 ---------------------------------------------------------
Warrant Exercise Price and the number of shares of Common Stock issuable upon
exercise of this Warrant shall be adjusted from time to time as follows:

          (a) Adjustment of Warrant Exercise Price and Number of Shares upon
              --------------------------------------------------------------
Issuance of Common Stock.  If and whenever on or after the date of issuance of
------------------------
this Warrant, the Company issues or sells, or in accordance with Section 8(b) is
deemed to have issued or sold, any shares of Common Stock (including the
issuance or sale of shares of Common Stock owned or held by or for the account
of the Company, but excluding shares of Common Stock deemed to have been issued
by the Company in connection with an Exempt Issuance or upon exercise or
conversion of the Other Securities) for consideration per share (the "Applicable
                                                                      ----------
Price") which is less than the Warrant Exercise Price in effect immediately
-----
prior to such time, then immediately after such issue or sale the Warrant
Exercise Price then in effect shall be reduced to an amount equal to the
Applicable Price.  Upon each such adjustment of the Warrant Exercise Price
hereunder, the number of Warrant Shares acquirable upon exercise of this Warrant
shall be adjusted to the number of shares determined by dividing (i) the product
of (x) the Warrant Exercise Price in effect immediately prior to such adjustment
and (y) the number of shares of Warrant Shares acquirable upon exercise of this
Warrant immediately prior to such adjustment by (ii) the Warrant Exercise Price
resulting from such adjustment.

          (b) Effect on Warrant Exercise Price of Certain Events.  For purposes
              --------------------------------------------------
of determining the adjusted Warrant Exercise Price under Section 8(a) above, the
following shall be applicable:

              (i) Issuance of Options.  If the Company in any manner grants any
                  -------------------
Options and the lowest price per share for which one share of Common Stock is
issuable upon the exercise of any such Option or upon conversion or exchange of
any Convertible Securities issuable upon exercise of any such Option is less
than the Warrant Exercise Price then in effect, then such share of Common Stock
shall be deemed to be outstanding and to have been issued and sold by the
Company at the time of the granting or sale of such Option for such price per
share.  For purposes of this Section 8(b)(i), the "lowest price per share for
which one share of Common Stock is issuable upon exercise of such Options or
upon conversion or exchange of such Convertible Securities" shall be equal to
the sum of the lowest amounts of consideration (if any) received or receivable
by the Company with respect to any one share of Common Stock upon the granting
or sale of the Option, upon exercise of the Option and upon conversion or
exchange of any Convertible Security issuable upon exercise of such Option. No
further adjustment of the Warrant Exercise Price shall be made upon the actual
issuance of such Common Stock or of such Convertible Securities upon the
exercise of such Options or upon the actual issuance of such Common Stock upon
conversion or exchange of such Convertible Securities.  Notwithstanding the
foregoing, no adjustment shall be made pursuant to this Section 8(b)(i) to the
extent that such adjustment is based solely on the fact that the Convertible
Securities issuable upon exercise of such Option are convertible into or
exchangeable for Common Stock at a price which varies with the market price of
the Common Stock.

              (ii) Issuance of Convertible Securities.  If the Company in any
                   ----------------------------------
manner issues or sells any Convertible Securities and the lowest price per share
for which one share of

                                       7
<PAGE>

Common Stock is issuable upon such conversion or exchange thereof is less than
the Warrant Exercise Price then in effect, then such share of Common Stock shall
be deemed to be outstanding and to have been issued and sold by the Company at
the time of the issuance or sale of such Convertible Securities for such price
per share. For the purposes of this Section 8(b)(ii), the "lowest price per
share for which one share of Common Stock is issuable upon such conversion or
exchange" shall be equal to the sum of the lowest amounts of consideration (if
any) received or receivable by the Company with respect to one share of Common
Stock upon the issuance or sale of the Convertible Security and upon conversion
or exchange of such Convertible Security. No further adjustment of the Warrant
Exercise Price shall be made upon the actual issuance of such Common Stock upon
conversion or exchange of such Convertible Securities, and if any such issue or
sale of such Convertible Securities is made upon exercise of any Options for
which adjustment of the Warrant Exercise Price had been or are to be made
pursuant to other provisions of this Section 8(b), no further adjustment of the
Warrant Exercise Price shall be made by reason of such issue or sale.
Notwithstanding the foregoing, no adjustment shall be made pursuant to this
Section 8(b)(ii) to the extent that such adjustment is based solely on the fact
that such Convertible Securities are convertible into or exchangeable for Common
Stock at a price which varies with the market price of the Common Stock.

              (iii)  Change in Option Price or Rate of Conversion.  If the
                     --------------------------------------------
purchase price provided for in any Options, the additional consideration, if
any, payable upon the issue, conversion or exchange of any Convertible
Securities, or the rate at which any Convertible Securities are convertible into
or exchangeable for Common Stock changes at any time, the Warrant Exercise Price
in effect at the time of such change shall be adjusted to the Warrant Exercise
Price which would have been in effect at such time had such Options or
Convertible Securities provided for such changed purchase price, additional
consideration or changed conversion rate, as the case may be, at the time
initially granted, issued or sold and the number of shares of Common Stock
acquirable hereunder shall be correspondingly readjusted. For purposes of this
Section 8(b)(iii), if the terms of any Option or Convertible Security that was
outstanding as of the date of issuance of this Warrant are changed in the manner
described in the immediately preceding sentence, then such Option or Convertible
Security and the Common Stock deemed issuable upon exercise, conversion or
exchange thereof shall be deemed to have been issued as of the date of such
change. No adjustment shall be made if such adjustment would result in an
increase of the Warrant Exercise Price then in effect.

              (iv) Treatment of Expired Options and Unexercised Convertible
                   --------------------------------------------------------
Securities.  If, in any case, the total number of shares of Common Stock
----------
issuable upon the exercise of any Option or upon exercise, conversion or
exchange of any Convertible Security is not, in fact, issued and the rights to
exercise such Option or to exercise, convert or exchange such Convertible
Securities shall have expired or terminated, the Warrant Exercise Price then in
effect will be readjusted to the Warrant Exercise Price which would have been in
effect at the time of such expiration or termination had such Option or
Convertible Securities, to the extent outstanding immediately prior to such
expiration or termination (other than in respect of the actual number of shares
of Common Stock issued upon exercise or conversion thereof) never been issued.

                                       8
<PAGE>

          (c) Effect on Warrant Exercise Price of Certain Events.  For purposes
              --------------------------------------------------
of determining the adjusted Warrant Exercise Price under Sections 8(a) and 8(b),
the following shall be applicable:

              (i) Calculation of Consideration Received.  In case any Option is
                  -------------------------------------
issued in connection with the issue or sale of other securities of the Company,
together comprising one integrated transaction in which no specific
consideration is allocated to such Options by the parties thereto, the Options
will be deemed to have been issued for a consideration of $.01.  If any Common
Stock, Options or Convertible Securities are issued or sold or deemed to have
been issued or sold for cash, the consideration received therefor will be deemed
to be the amount received by the Company therefor before deduction of reasonable
commissions, underwriting discounts or allowances or other similar reasonable
expenses incurred by the Company.  If any Common Stock, Options or Convertible
Securities are issued or sold for a consideration other than cash, the amount of
such consideration received by the Company will be the fair value of such
consideration, except where such consideration consists of securities that are
listed for trading on a national securities exchange or automated quotation
system, in which case the amount of consideration received by the Company will
be the average market price of such securities for the twenty (20) consecutive
trading days immediately preceding the date of receipt.  If any Common Stock,
Options or Convertible Securities are issued to the owners of the non-surviving
entity in connection with any merger in which the Company is the surviving
entity, the amount of consideration therefor will be deemed to be the fair value
of such portion of the net assets and business of the non-surviving entity as is
attributable to such Common Stock, Options or Convertible Securities, as the
case may be.  The fair value of any consideration other than cash or securities
that are listed for trading on a national securities exchange or automated
quotation system will be determined jointly by the Company and the holders of
Warrants representing a majority of the shares of Common Stock obtainable upon
exercise of the Warrants then outstanding.  If such parties are unable to reach
agreement within ten (10) days after the occurrence of an event requiring
valuation (the "Valuation Event"), the fair value of such consideration will be
                ---------------
determined within five Business Days after the tenth (10th) day following the
Valuation Event by an independent, reputable appraiser jointly selected by the
Company and the holders of Warrants representing two-thirds majority of the
shares of Common Stock obtainable upon exercise of the Warrants then
outstanding.  The determination of such appraiser shall be final and binding
upon all parties and the fees and expenses of such appraiser shall be borne by
the Company.

              (ii) Record Date.  If the Company takes a record of the holders of
                   -----------
Common Stock for the purpose of entitling them (1) to receive a dividend or
other distribution payable in Common Stock, Options or in Convertible Securities
or (2) to subscribe for or purchase Common Stock, Options or Convertible
Securities, then such record date will be deemed to be the date of the issue or
sale of the shares of Common Stock deemed to have been issued or sold upon the
declaration of such dividend or the making of such other distribution or the
date of the granting of such right of subscription or purchase, as the case may
be.

          (d) Adjustment of Warrant Exercise Price upon Subdivision or
              --------------------------------------------------------
Combination of Common Stock.  If the Company at any time after the date of
---------------------------
issuance of this Warrant subdivides (by any stock split, stock dividend,
recapitalization or otherwise) one or more classes

                                       9
<PAGE>

of its outstanding shares of Common Stock into a greater number of shares, the
Warrant Exercise Price in effect immediately prior to such subdivision will be
proportionately reduced and the number of shares of Common Stock obtainable upon
exercise of this Warrant will be proportionately increased. If the Company at
any time after the date of issuance of this Warrant combines (by combination,
reverse stock split or otherwise) one or more classes of its outstanding shares
of Common Stock into a smaller number of shares, the Warrant Exercise Price in
effect immediately prior to such combination will be proportionately increased
and the number of shares of Common Stock obtainable upon exercise of this
Warrant will be proportionately decreased.

          (e) Distribution of Assets.  If the Company shall declare or make any
              ----------------------
distribution of its assets (or rights to acquire its assets) to holders of
Common Stock as a partial liquidating dividend, by way of return of capital or
otherwise (including, without limitation, any distribution of cash, property or
securities of a subsidiary) (a "Distribution"), at any time after the issuance
                                ------------
of this Warrant, then, in each such case:

              (i) the Warrant Exercise Price in effect immediately prior to the
close of business on the record date fixed for the determination of holders of
Common Stock entitled to receive the Distribution shall be reduced, effective as
of the close of business on such record date, to a price determined by
multiplying such Warrant Exercise Price by a fraction of which (A) the numerator
shall be the closing bid price on the trading day immediately preceding such
record date minus the value of the Distribution (as determined in good faith by
the Company's Board of Directors) applicable to one share of Common Stock, and
(B) the denominator shall be the closing bid price on the trading day
immediately preceding such record date; and

              (ii) either (A) the number of Warrant Shares obtainable upon
exercise of this Warrant shall be increased to a number of shares equal to the
number of shares of Common Stock obtainable immediately prior to the close of
business on the record date fixed for the determination of holders of Common
Stock entitled to receive the Distribution multiplied by the reciprocal of the
fraction set forth in the immediately preceding clause (i), or (B) in the event
that the Distribution is of common stock of a company whose common stock is
traded on a national securities exchange or a national automated quotation
system, then the holder of this Warrant shall receive an additional warrant to
purchase Common Stock, the terms of which shall be identical to those of this
Warrant, except that such warrant shall be exercisable into the amount of the
assets that would have been payable to the holder of this Warrant pursuant to
the Distribution had the holder exercised this Warrant immediately prior to such
record date and with an exercise price equal to the amount by which the exercise
price of this Warrant was decreased with respect to the Distribution pursuant to
the terms of the immediately preceding clause (i).

          (f) Certain Events.  If any event occurs of the type contemplated by
              --------------
the provisions of this Section 8 but not expressly provided for by such
provisions (including, without limitation, the granting of stock appreciation
rights, phantom stock rights or other rights with equity features), then the
Company's Board of Directors will make an appropriate adjustment in the Warrant
Exercise Price and the number of Warrant Shares obtainable upon exercise of this
Warrant so as to protect the rights of the holders of the Warrants; provided
that no such

                                      10
<PAGE>

adjustment will increase the Warrant Exercise Price or decrease the number of
shares of Common Stock obtainable as otherwise determined pursuant to this
Section 8.

          (g)  Notices.
               -------

               (i) Immediately upon any adjustment of the Warrant Exercise
Price, the Company will give written notice thereof to the holder of this
Warrant, setting forth in reasonable detail, and certifying, the calculation of
such adjustment.

               (ii) The Company will give written notice to the holder of this
Warrant at least twenty (20) days prior to the date on which the Company closes
its books or takes a record (A) with respect to any dividend or distribution
upon the Common Stock, (B) with respect to any pro rata subscription offer to
holders of Common Stock or (C) for determining rights to vote with respect to
any Organic Change (as defined below), dissolution or liquidation, provided that
such information shall be made known to the public prior to or in conjunction
with such notice being provided to such holder.

               (iii)  The Company will also give written notice to the holder
of this Warrant at least twenty (20) days prior to the date on which any Organic
Change (as defined below), dissolution or liquidation will take place, provided
that such information shall be made known to the public prior to or in
conjunction with such notice being provided to such holder.

     Section 9.  Purchase Rights; Reorganization, Reclassification,
                 --------------------------------------------------
Consolidation, Merger or Sale.
-----------------------------

          (a) If at any time after the date hereof, the Company grants, issues
or sells any Options, Convertible Securities or rights to purchase stock,
warrants, securities or other property pro rata to the record holders of any
class of Common Stock (the "Purchase Rights"), then the holder of this Warrant
                            ---------------
will be entitled to acquire, upon the terms applicable to such Purchase Rights,
the aggregate Purchase Rights which such holder could have acquired if such
holder had held the number of shares of Common Stock acquirable upon complete
exercise of this Warrant immediately before the date on which a record is taken
for the grant, issuance or sale of such Purchase Rights, or, if no such record
is taken, the date as of which the record holders of Common Stock are to be
determined for the grant, issue or sale of such Purchase Rights.

          (b) Any recapitalization, reorganization, reclassification,
consolidation, merger, sale of all or substantially all of the Company's assets
to another Person or other transaction which is effected in such a way that
holders of Common Stock are entitled to receive (either directly or upon
subsequent liquidation) stock, securities or assets with respect to or in
exchange for Common Stock is referred to herein as "Organic Change."  Prior to
                                                    --------------
the consummation of any (i) sale of all or substantially all of the Company's
assets to an acquiring Person or (ii) other Organic Change following which the
Company is not a surviving entity, the Company will use its best efforts to
secure from the Person purchasing such assets or the successor resulting from
such Organic Change (in each case, the "Acquiring Entity") written agreement (in
                                        ----------------
form and substance satisfactory to the holders of Warrants representing a
majority of the shares of Common Stock obtainable upon exercise of the Warrants
then outstanding) to


                                      11
<PAGE>

deliver to each holder of Warrants in exchange for such Warrants, a security of
the Acquiring Entity evidenced by a written instrument substantially similar in
form and substance to this Warrant and satisfactory to the holders of the
Warrants (including, an adjusted warrant exercise price equal to the value for
the Common Stock reflected by the terms of such consolidation, merger or sale,
and exercisable for a corresponding number of shares of Common Stock acquirable
and receivable upon exercise of the Warrants, if the value so reflected is less
than the Warrant Exercise Price in effect immediately prior to such
consolidation, merger or sale). Prior to the consummation of any other Organic
Change, the Company shall use its best efforts to make appropriate provision (in
form and substance satisfactory to the holders of Warrants representing a
majority of the shares of Common Stock obtainable upon exercise of the Warrants
then outstanding) to ensure that each of the holders of the Warrants will
thereafter have the right to acquire and receive in lieu of or in addition to
(as the case may be) the Warrant Shares immediately theretofore acquirable and
receivable upon the exercise of such holder's Warrants, such shares of stock,
securities or assets that would have been issued or payable in such Organic
Change with respect to or in exchange for the number of Warrant Shares which
would have been acquirable and receivable upon the exercise of such holder's
Warrant as of the date of such Organic Change (without taking into account any
limitations or restrictions on the exercisability of this Warrant).

          (c) In the event the Company proposes to effect an Organic Change,
then in addition to any other rights the holder may have, the holder shall have
the right to effect a Cashless Exercise (as defined below), by presentation and
surrender of this Warrant to the Company at its principal executive offices with
a written notice of the holder's intention to effect a Cashless Exercise,
including a calculation of the number of shares of Common Stock to be issued
upon such exercise in accordance with the terms hereof.  A "Cashless Exercise"
                                                            -----------------
shall mean that, in lieu of paying the Warrant Exercise Price in cash, the
holder shall surrender this Warrant for that number of Warrant Shares determined
by subtracting from the number of Warrant Shares otherwise issuable to the
holder upon such exercise, an amount of Warrant Shares (the "Surrendered
                                                             -----------
Shares") having a closing bid price (as reported by Bloomberg) on the date
------
immediately preceding the date of the exercise notice equal to the Aggregate
Exercise Price (as defined in Section 2) of the Warrant Shares for which this
Warrant is being exercised; and thereafter the Surrendered Shares shall no
longer be available for issuance hereunder.

     Section 10.  Lost, Stolen, Mutilated or Destroyed Warrant.  If this Warrant
                  --------------------------------------------
is lost, stolen, mutilated or destroyed, the Company shall, on receipt of an
indemnification undertaking, issue a new Warrant of like denomination and tenor
as this Warrant so lost, stolen, mutilated or destroyed.

     Section 11.  Notice.  Any notices, consents, waivers or other
                  ------
communications required or permitted to be given under the terms of this Warrant
must be in writing and will be deemed to have been delivered:  (i) upon receipt,
when delivered personally; (ii) upon receipt, when sent by facsimile (provided
confirmation of transmission is mechanically  or electronically generated and
kept on file by the sending party); or (iii) one Business Day after deposit with
a nationally recognized overnight delivery service, in each case properly
addressed to the party to receive the same.  The addresses and facsimile numbers
for such communications shall be:
<PAGE>

          If to the Company:

                Data Race Inc.
                6509 Windcrest Drive, Suite 120
                Plano, Texas 75024
                Telephone:    (972) 205-4005
                Facsimile:    (210) 558-0356
                Attention:    James G. Scogin

          With copy to:

                Jackson Walker LLP
                901 Main Street, Suite 6000
                Dallas, Texas 75202
                Telephone:     (214) 953 - 5801
                Facsimile:     (214) 953 - 5736
                Attention:     James S. Ryan, III, Esq.

If to a holder of this Warrant, to it at the address and facsimile number set
forth on the Schedule of Buyers to the Securities Purchase Agreement, with
copies to such holder's representatives as set forth on such Schedule of Buyers,
or at such other address and facsimile as shall be delivered to the Company upon
the issuance or transfer of this Warrant.  Each party shall provide five days'
prior written notice to the other party of any change in address or facsimile
number.  Written confirmation of receipt (A) given by the recipient of such
notice, consent, waiver or other communication, (B) mechanically or
electronically generated by the sender's facsimile machine containing the time,
date, recipient facsimile number and an image of the first page of such
transmission or (C) provided by a nationally recognized overnight delivery
service shall be rebuttable evidence of personal service, receipt by facsimile
or receipt from a nationally recognized overnight delivery service in accordance
with clause (i), (ii) or (iii) above, respectively.

     Section 12.  [Omitted]

     Section 13.  Date.  The date of this Warrant is May 11, 2001.  This
                  ----
Warrant, in all events, shall be wholly void and of no effect after the close of
business on the Expiration Date, except that notwithstanding any other
provisions hereof, the provisions of Section 7 shall continue in full force and
effect after such date as to any Warrant Shares or other securities issued upon
the exercise of this Warrant.

     Section 14.  Amendment and Waiver.  Except as otherwise provided herein,
                  --------------------
the provisions of the Warrants may be amended and the Company may take any
action herein prohibited, or omit to perform any act herein required to be
performed by it, only if the Company has obtained the written consent of the
holders of Warrants representing two-thirds of the shares of Common Stock
obtainable upon exercise of the Warrants then outstanding; provided that no such
action may increase the Warrant Exercise Price of the Warrants or decrease the
number of

                                      13
<PAGE>

shares or class of stock obtainable upon exercise of any Warrants without the
written consent of the holder of such Warrant.

     Section 15.  Descriptive Headings; Governing Law.  The descriptive headings
                  -----------------------------------
of the several Sections and paragraphs of this Warrant are inserted for
convenience only and do not constitute a part of this Warrant.  This Warrant
shall be governed by the internal laws of the State of Texas, without giving
effect to any choice of law or conflict of law provision or rule (whether of the
State of Texas or any other jurisdictions) that would cause the application of
the laws of any jurisdictions other than the State of Texas.


                                 [Signature Page Follows]

                                      14

<PAGE>

This Warrant has been duly executed by the Company as of the date first set
forth above.


                                    DATA RACE INC.


                                    By:
                                       -------------------------------
                                    Name:  James G. Scogin
                                         ------------------------------
                                    Title: Senior Vice President, Chief
                                           Financial Officer

                                      15

<PAGE>

                             EXHIBIT A TO WARRANT
                             --------------------

                               SUBSCRIPTION FORM
        TO BE EXECUTED BY THE REGISTERED HOLDER TO EXERCISE THIS WARRANT
                                 DATA RACE INC.

     The undersigned holder hereby exercises the right to purchase
_________________ of the shares of Common Stock ("Warrant Shares") of Data Race
Inc., a Texas corporation (the "Company"), evidenced by the attached Warrant
(the "Warrant").  Capitalized terms used herein and not otherwise defined shall
have the respective meanings set forth in the Warrant.

     1.  Payment of Warrant Exercise Price.  The holder shall pay the sum of
$___________________ to the Company in accordance with the terms of the Warrant.

     2.  Delivery of Warrant Shares.  The Company shall deliver to the holder
__________ Warrant Shares in accordance with the terms of the Warrant.



Date:___________ ______, _______



Name of Registered Holder

By:
   --------------------------
Name:
     ------------------------
Title:
      -----------------------


                                      16

<PAGE>

                              EXHIBIT B TO WARRANT
                              --------------------

                             FORM OF WARRANT POWER


FOR VALUE RECEIVED, the undersigned does hereby assign and transfer to
________________, Federal Identification No. __________, a warrant to purchase
____________ shares of the capital stock of Data Race Inc., a Texas corporation,
represented by warrant certificate no. _____, standing in the name of the
undersigned on the books of said corporation.  The undersigned does hereby
irrevocably constitute and appoint ______________, attorney to transfer the
warrants of said corporation, with full power of substitution in the premises.


Dated:  _________, 200_





                              -----------------------------------
                              By:
                                 --------------------------------
                              Name:
                                   ------------------------------
                              Title:
                                    -----------------------------

                                      17