<PAGE>

                                                                    EXHIBIT 10.6


                                    WARRANT


THE SECURITIES REPRESENTED BY THIS WARRANT 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 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 AN OPINION OF COUNSEL IN
FORM, REASONABLY ACCEPTABLE TO THE ISSUER THAT REGISTRATION IS NOT REQUIRED
UNDER THE 1933 ACT OR UNLESS SOLD PURSUANT TO RULE 144 UNDER SAID ACT.  ANY SUCH
OFFER, SALE, ASSIGNMENT OR TRANSFER MUST ALSO COMPLY WITH THE APPLICABLE STATE
SECURITIES LAWS.


                                DATA RACE INC.

                       Warrant To Purchase Common Stock

Warrant No.: 2000-D-04                                  Number of Shares: 78,637
Date of Issuance: June 12, 2000


Data Race Inc., a Texas corporation (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, EURAM CAP STRAT.
"A" FUND LIMITED, 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) 78,637 fully paid nonassessable shares of Common Stock (as defined
herein) of the Company (the "Warrant Shares") at the purchase price per share
provided in Section 1(b) below.

     Section 1.

          (a) Securities Purchase Agreement.  This Warrant is one of the
              -----------------------------
Warrants (the "Warrants") issued pursuant to the terms of that certain
Securities Purchase Agreement dated as of June 12, 2000, 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:
<PAGE>

               (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.

               (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 Warrants.

               (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, (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 two (2) 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 Chicago or
the State of Illinois 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)   "Options" means any rights, warrants or options to
subscribe for or purchase Common Stock or Convertible Securities.

               (vii)  "Other Securities" means (i) the other Warrants and (ii)
the shares of Common Stock issued from time to time pursuant to the Securities
Purchase Agreement.

               (viii) "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.

                                      -2-
<PAGE>

               (ix)  "Principal Market" means the Nasdaq National Market.

               (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 $5.45 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 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") in cash or by check or wire
transfer, 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.  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 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

                                      -3-
<PAGE>

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 .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.

          (e) Limitation on Beneficial Ownership.  The Company shall not effect
              ----------------------------------
any exercise of this Warrant and no holder of this Warrant shall have the right
to exercise this Warrant pursuant to Section 2 to the extent that after giving
effect to such exercise such Person (together with such Person's affiliates) (A)
would beneficially own in excess of 4.9% of the outstanding shares of the Common
Stock following such exercise and (B) would have acquired, through exercise of
this Warrant or otherwise, in excess of  4.9% of the outstanding shares of the
Common Stock following such exercise during the 60-day period ending on and
including such date of exercise.  For purposes of the foregoing sentence, the
number of shares of Common Stock beneficially owned by a Person and its
affiliates or acquired by a Person and its affiliates, as the case may be, shall
include the number of shares of Common Stock issuable upon exercise of this
Warrant with respect to which the determination of such sentence is being made,
but shall exclude the number of shares of Common Stock which would be issuable
upon (i) exercise of the remaining, non-exercised Warrant beneficially owned by
such Person and its affiliates and (ii) exercise or conversion of the
unexercised or unconverted portion of any other securities of the Company
(including, without limitation, any warrants) subject to a limitation on
conversion or exercise analogous to the limitation contained herein beneficially
owned by such Person and its affiliates.  Except as set forth in the preceding
sentence, for purposes of this Section 2(e), beneficial ownership shall be
calculated in accordance with Section 13(d) of the Securities Exchange Act of
1934, as amended.  Notwithstanding anything to the contrary contained herein,
each Exercise Notice shall constitute a representation by the holder submitting
such Exercise Notice that, after giving effect to such Exercise Notice, (A) the
holder will not beneficially own (as determined in accordance with this Section
2(e)) and (B) during the 60-day

                                      -4-
<PAGE>

period ending on and including such date of exercise, the holder will not have
acquired, through exercise of this Warrant or otherwise, a number of shares of
Common Stock in excess of 4.9% of the outstanding shares of Common Stock as
reflected in the Company's most recent Form 10-Q or Form 10-K, as the case may
be, or more recent public press release or other public notice by the Company
setting forth the number of shares of Common Stock outstanding, but after giving
effect to exercise of this Warrant by such holder since the date as of which
such number of outstanding shares of Common Stock was reported.

     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.

          (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 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 shares of Common Stock 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

                                      -5-
<PAGE>

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

     Section 6.  Representations of Holder.  The holder of this Warrant, by the
                 -------------------------
acceptance hereof, represents that it is acquiring this Warrant and the Warrant
Shares for its own account for investment only and not with a view towards, or
for resale in connection with, the public sale or distribution of this Warrant
or the Warrant Shares, except pursuant to sales registered or exempted under the
Securities Act; provided, however, that by making the representations herein,
the holder does not agree to hold this Warrant or any of the Warrant Shares for
any minimum or other specific term and reserves the right to dispose of this
Warrant and the Warrant Shares at any time in accordance with or pursuant to a
registration statement or an exemption under the Securities Act.  The holder of
this Warrant further represents, by acceptance hereof, that, as of this date,
such holder is an  "accredited investor" as such term is defined in Rule 501(a)
of Regulation D promulgated by the Securities and Exchange Commission under the
Securities Act (an "Accredited Investor").

     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.

                                      -6-
<PAGE>

          (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
June 12, 2000 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.

                                      -7-
<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 a consideration per share less than the
Warrant Exercise Price in effect immediately prior to such time (the "Applicable
Price"), then immediately after such issue or sale the Warrant Exercise Price
then in effect shall be reduced to an amount equal to the product of (x) the
Warrant Exercise Price in effect immediately prior to such issue or sale and (y)
the quotient determined by dividing (1) the sum of (I) the product derived by
multiplying the Applicable Price by the number of shares of Common Stock Deemed
Outstanding immediately prior to such issue or sale, plus (II) the
consideration, if any, received by the Company upon such issue or sale, by (2)
the product derived by multiplying the (I) Applicable Price by (II) the number
of shares of Common Stock Deemed Outstanding immediately after such issue or
sale.  Upon each such adjustment of the Warrant Exercise Price hereunder, the
number of shares of Common Stock acquirable upon exercise of this Warrant shall
be adjusted to the number of shares determined by multiplying the Warrant
Exercise Price in effect immediately prior to such adjustment by the number of
shares of Common Stock acquirable upon exercise of this Warrant immediately
prior to such adjustment and dividing the product thereof by 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 Applicable Price, 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

                                      -8-
<PAGE>

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 Common Stock is issuable upon such conversion or exchange
thereof is less than the Applicable Price, 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

                                      -9-
<PAGE>

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.

          (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, in which
case the amount of consideration received by the Company will be the 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
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 a 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

                                      -10-
<PAGE>

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 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).

                                      -11-
<PAGE>

          (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 shares of Common Stock obtainable upon exercise
of this Warrant so as to protect the rights of the holders of the Warrants;
provided that no such 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, 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.

                                      -12-
<PAGE>

     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 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 insure 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 shares of Common Stock 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 shares of Common Stock 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
exerciseability 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

                                      -13-
<PAGE>

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:

          If to the Company:

               Data Race Inc.
               12400 Network Blvd.
               San Antonio, TX 78249-3341
               Telephone: (210) 263-2000
               Facsimile: (210) 558-0365
               Attention: Jim Scogin

          With copy to:

               Akin, Gump, Strauss, Hauer & Feld, L.L.P.
               300 Convent Street, Suite 1500
               San Antonio, Texas 78205
               Telephone: (210) 281-7000
               Facsimile: (210) 224-2035
               Attention: Pat Ryan, Esq.

                                      -14-
<PAGE>

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.  [Reserved.]

     Section 13.  Date.  The date of this Warrant is June 12, 2000.  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 a majority 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 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 Illinois, without giving
effect to any choice of law or conflict of law provision or rule (whether of the
State of Illinois or any other jurisdictions) that would cause the application
of the laws of any jurisdictions other than the State of Illinois.


                           [Signature Page Follows]

                                      -15-
<PAGE>

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


                                        DATA RACE INC.


                                        By: /s/ James G. Scogin
                                        Name:  James G. Scogin
                                        Title: SVP - Chief Financial Officer
<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:_____________________
<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:_______________________