Document:

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                                                                     EXHIBIT 4.1

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COMMON STOCK                 COMPUTER DISCOUNT                    COMMON STOCK
                                [CDW logo]
------------                   WAREHOUSE/TM/                      ------------
   NUMBER                                                            SHARES
 CDW 10881
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INCORPORATED UNDER THE LAWS OF                                SEE REVERSE FOR
   THE STATE OF ILLINOIS                                    CERTAIN DEFINITIONS

                          CDW COMPUTER CENTERS, INC.
                                                             CUSIP 125129 10 6

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  THIS CERTIFIES THAT

                                   SPECIMEN

  IS THE OWNER OF

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FULLY PAID AND NON-ASSESSABLE SHARES OF COMMON STOCK WITH THE PAR VALUE OF $.01
PER SHARE OF
--------------------------CDW COMPUTER CENTERS, INC.----------------------------
transferable on the books of the Corporation in person or by attorney duly
authorized in writing upon surrender of this certificate properly endorsed. This
certificate and the shares represented hereby are issued and shall be held
subject to all the provisions of the Corporation's Certificate of Incorporation
and any amendments thereof, copies of which are on file with the Transfer Agent
to all the provisions to which the holder hereof by acceptance of this
certificate assents.

  This certificate is not valid until countersigned by the Transfer Agent and
  registered by the Registrant.

  WITNESS the facsimile seal of the Corporation and the facsimile signature of
  its duly authorized officers.

Dated:

/s/ John A. Edwardson         [CDW COMPUTER CENTERS, INC.   /s/ Gregory C. Zeman
  CHIEF EXECUTIVE OFFICER            CORPORATE SEAL                PRESIDENT
                                       ILLINOIS]

Countersigned and Registered:
                    AMERICAN STOCK TRANSFER A TRUST COMPANY
                             (Brooklyn, New York)
                                                                  Transfer Agent
                                                                   and Registrar

                                            By
                                                            Authorized Signature
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                          CDW COMPUTER CENTERS, INC.

     UPON WRITTEN REQUEST, THE CORPORATION WILL FURNISH THE SHAREHOLDER, WITHOUT
CHARGE, A DESCRIPTION OF THE DESIGNATIONS, RELATIVE RIGHTS, PREFERENCES, AND
LIMITATIONS APPLICABLE TO EACH CLASS; AND THE VARIATIONS IN RIGHTS, PREFERENCES,
AND LIMITATIONS DETERMINED FOR EACH SERIES; AND THE AUTHORITY OF THE BOARD OF
DIRECTORS TO DETERMINE VARIATIONS FOR FUTURE SERIES OR CLASSES, OF THE
CORPORATION'S AUTHORIZED STOCK.

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     The following abbreviations, when used in the inception on the face of this
certificate, shall be construed as though they were written out in full
according to applicable laws or regulations.
<TABLE>
          <S>                                                <C>
          TEN COM- as tenants in common                      UNIF GIFT MIN ACT           Custodian
          TEN ENT- as tenants by the entireties                                ----------          ---------------
           JT TEN- as joint tenants with                                         (Cust)                 (Minor)
                   right of survivorship and                                     under Uniform Gifts to Minors
                   not as tenants in common
                                                                                 Act
                                                                                     ----------------------------
                                                                                                (State)

                              Additional abbreviations may also be used though not in the above list
</TABLE>

     For Value received,                                hereby sold, assign and
                         ------------------------------
transfer unto

PLEASE INSERT SOCIAL SECURITY OR OTHER
    IDENTIFYING NUMBER OF ASSIGNEE
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            PLEASE PRINT OR TYPEWRITE NAME AND ADDRESS OF ASSIGNEE
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                                                                          Shares
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of the Common Stock represented by the within Certificate, and do hereby
irrevocably constitute and appoint                                    Attorney,
                                  -----------------------------------
to transfer the said shares on the books of the within named corporation with
full power of substitution.

Dated,
       ---------------------

                           X
                            ---------------------------------------------------

                           X
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                           NOTICE: THE SIGNATURE(S) TO THIS ASSIGNMENT MUST
                           CORRESPOND WITH THE NAME(S) AS WRITTEN UPON THE FACE
                           OF THE CERTIFICATE, IN EVERY PARTICULAR, WITHOUT
                           ALTERATION OR ENLARGEMENT OR ANY CHANGE WHATSOEVER.

   SIGNATURE(S) GUARANTEED:
                            ---------------------------------------------------
                            THE SIGNATURE(S) SHOULD BE GUARANTEED BY AN ELIGIBLE
                            GUARANTOR INSTITUTION, (BANKS, STOCKBROKERS, SAVINGS
                            AND LOAN ASSOCIATIONS, AND CREDIT UNIONS WITH
                            MEMBERSHIP IN AN APPROVED SIGNATURE GUARANTEE
                            MEDALLION PROGRAM, PURSUANT TO S.E.C. RULE 17A8-15.

KEEP THIS CERTIFICATE IN A SAFE PLACE, IF IT IS LOST, STOLEN, OR DESTROYED, THE
CORPORATION MAY REQUIRE A BOND OF INDEMNITY AS A CONDITION TO THE ISSUANCE OF A
REPLACEMENT CERTIFICATE.<PAGE>   1
                                                                     EXHIBIT 4.1

THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER
THE SECURITIES ACT OF 1933, AS AMENDED. SUCH SECURITIES MAY NOT BE SOLD OR
TRANSFERRED IN THE ABSENCE OF SUCH REGISTRATION OR AN EXEMPTION THEREFROM UNDER
SAID ACT.

                                                             Warrant to Purchase

WE-022                                                             20,000 Shares

                             NTN COMMUNICATIONS INC.

             (Incorporated under the laws of the State of Delaware)

                WARRANT CERTIFICATE FOR THE PURCHASE OF SHARES OF
           THE $.005 PAR VALUE COMMON STOCK OF NTN COMMUNICATIONS INC.

                    EXERCISABLE ONLY AFTER APRIL 30, 2001 AND
                            VOID AFTER APRIL 1, 2004.

Warrant Price:  $0.50  (Fifty Cents) per share.

         1. THIS IS TO CERTIFY that, for value received, BARON ENTERPRISES, INC.
(the "Holder"), is entitled to purchase, subject to the terms and conditions
hereinafter set forth, at any time after April 30, 2001 and on or before April
1, 2004 (the "Warrant Period"), up to 20,000 shares of the $.005 par value
common stock ("Common Stock") of NTN Communications Inc. (the "Company"), and to
receive certificate(s) for the Common Stock so purchased. This Warrant shall
become vested and exercisable as to one twelfth (1/12) of the total number of
shares on the last day of each of the twelve (12) consecutive months beginning
with, and immediately subsequent to, April 30, 2001, subject to the Holder
continuing to provide advertising sales representation services pursuant to the
Advertising Sales Representative Agreement, dated as of May 8, 2001, by and
between the Holder and NTN Communications, Inc. This Warrant may be exercised in
whole or in part. Such exercise shall be accomplished by tender to the Company
of the purchase price set forth above as the warrant price (the "Warrant
Price"), either in cash or by certified check or bank cashier's check, payable
to the order of the Company, together with presentation and surrender to the
Company of this Warrant with an executed subscription in substantially the form
attached hereto as Exhibit A. Fractional shares of the Company's Common Stock
will not be issued upon the exercise of this Warrant.

         2. The Company agrees at all times to reserve and hold available out of
the aggregate of its authorized but unissued Common Stock the number of shares
of its Common Stock issuable upon the exercise of this and all other Warrants of
like tenor then outstanding. The Company further covenants and agrees that all
shares of Common Stock that may be delivered upon the exercise of this Warrant
will, upon delivery, be fully paid and nonassessable and free from all taxes,
liens and charges with respect to the purchase thereof hereunder.

<PAGE>   2

         This Warrant and the Common Stock issuable upon the exercise hereof may
not be sold, transferred, pledged or hypothecated unless the Company shall have
been supplied with evidence reasonably satisfactory to it that such transfer is
not in violation of the Securities Act of 1933, as amended (the "Act") or any
applicable state laws. Subject to the satisfaction of the aforesaid condition,
this Warrant shall be transferable by the Holder.

         If this Warrant is transferred, in whole or in part, upon surrender of
this Warrant to the Company, the Company shall deliver to each transferee a
Warrant evidencing the rights of such transferee to purchase the number of
shares of Common Stock that such transferee is entitled to purchase pursuant to
such transfer.

         The Company may place a legend on this Warrant or any replacement
Warrant and on each certificate representing shares issuable upon exercise of
this Warrant as to which the Company has not been supplied evidence that the
transfer of such security would not be in violation of the Act and any
applicable state laws.

         3. This Warrant does not entitle the Holder to any voting rights or
other rights as a stockholder of the Company, nor to any other rights whatsoever
except the rights herein set forth, and no dividend shall be payable or accrue
by reason of this Warrant or the interest represented hereby, or the shares
purchasable hereunder, until or unless, and except to the extent that, this
Warrant is exercised.

         4. This Warrant is exchangeable upon its surrender by the Holder to the
Company for new Warrants of like tenor and date representing in the aggregate
the right to purchase the number of shares purchasable hereunder, each of such
new Warrants to represent the right to purchase such number of shares as may be
designated by the Holder at the time of such surrender.

         The Company shall comply with the reporting requirements of Sections 13
and 15(d) of the Securities Exchange Act of 1934 (the "Exchange Act") for so
long as and to the extent that such requirements apply to the Company.

         5. The Warrant Price and the number of shares purchasable upon the
exercise of this Warrant are subject to adjustment from time to time upon the
occurrence of any of the events specified in this Section 5.

<PAGE>   3

                  (a) In case the Company shall (i) pay a dividend in shares of
Common Stock or make a distribution in shares of Common Stock, (ii) subdivide
its outstanding shares of Common Stock, (iii) combine its outstanding shares of
Common Stock into a smaller number of shares of Common Stock, or (iv) issue by
reclassification of its shares of Common Stock other securities of the Company,
the number of shares of Common Stock purchasable upon exercise of this Warrant
immediately prior thereto shall be adjusted so that the Holder of this Warrant
shall be entitled to receive the kind and number of shares of Common Stock or
other securities of the Company that he would have owned or have been entitled
to receive after the happening of any of the events described above, had such
Warrant been exercised immediately prior to the happening of such event or any
record date with respect thereto. An adjustment made pursuant to this paragraph
(a) shall become effective immediately after the effective date of such event
retroactive to the record date, if any, for such event.

                  (b) Whenever the number of shares of Common Stock purchasable
upon the exercise of this Warrant is adjusted, as herein provided, the Warrant
Price shall be adjusted by multiplying such Warrant Price immediately prior to
such adjustment by a fraction, of which the numerator shall be the number of
shares of Common Stock purchasable upon the exercise of this Warrant immediately
prior to such adjustment, and of which the denominator shall be the number of
shares of Common Stock so purchasable immediately thereafter.

                  (c) For the purpose of this Section 5, the term shares of
Common Stock shall mean (i) the class of stock designated as the Common Stock of
the Company at the date of this Warrant, or (ii) any other class of stock
resulting from successive changes or reclassifications of such shares consisting
solely of change in par value, or from par value to no par value, or from no par
value to par value.

                  (d) If during the Warrant Period the Company consolidates with
or merges into another corporation or transfers all or substantially all of its
assets, the Holder shall thereafter be entitled upon exercise hereof to
purchase, with respect to each share of Common Stock purchasable hereunder
immediately prior to the date upon which such consolidation or merger becomes
effective, the securities or property to which a holder of shares of Common
Stock is entitled upon such consolidation or merger, without any change in, or
payment in addition to the Warrant Price in effect immediately prior to such
merger or consolidation, and the Company shall take such steps in connection
with such consolidation or merger as may be necessary to ensure that all of the
provisions of this Warrant shall thereafter be applicable, as nearly as
reasonably may be, in relation to any securities or property thereafter
deliverable upon the exercise of this Warrant. The Company shall not effect any
such consolidation, merger or asset transfer unless prior to the consummation
thereof the successor corporation resulting therefrom shall assume by written
agreement executed and mailed to the registered Holder at his address shown on
the books and records of the Company, the obligation to deliver to such Holder
any such securities or property as in accordance with the foregoing provisions
such Holder shall be entitled to purchase.

<PAGE>   4

                  (e) Upon the happening of any event requiring an adjustment of
the Warrant Price, the Company shall forthwith give written notice thereof to
the registered Holder of this Warrant, stating the adjusted Warrant Price and
the adjusted number of shares of Common Stock or other securities or property
purchasable upon the exercise hereof resulting from such event and setting forth
in reasonable detail the method of calculation and the facts upon which such
calculation is based. The Board of Directors of the Company shall determine the
adjusted Warrant Price and the securities or property purchasable upon exercise.
If any voluntary or involuntary dissolution, liquidation, or winding up of the
Company is proposed, the Company shall give at least 20 days prior written
notice of such proposal to the registered Holder hereof stating the date on
which such event is to take place and the date (which shall be at least 20 days
after giving of such notice) as of which the holders of shares of Common Stock
of record shall be entitled to exchange their Common Stock for securities or
other property deliverable upon such dissolution, liquidation or winding up.
This Warrant and all rights hereunder shall terminate as of the date on which
such dissolution, liquidation, or winding up takes place. The notices pursuant
to this paragraph shall be given by first class mail, postage prepaid, addressed
to the registered Holder of this Warrant at his address appearing in the records
of the Company.

                  (f) Irrespective of any adjustments pursuant to this Section 4
to the Warrant Price or to the number of shares or other securities or other
property obtainable upon exercise of this Warrant, this Warrant may continue to
state the Warrant Price and the number of shares obtainable upon exercise, as
the same price and number of shares stated herein.

         6. Notwithstanding anything to the contrary herein the Exercise Dates
shall automatically be accelerated immediately upon a Change in Control Event. A
"Change in Control Event" shall mean:

         (1) The acquisition by any individual entity or group (within the
meaning of Section 13(d)(3) or 14(d)(2) of the Exchange Act (a "Person")) of
beneficial ownership of 50% or more of the then outstanding voting securities of
the Corporation entitled to vote generally in the election of directors (the
"Outstanding Voting Securities"); provided, however, that the following
acquisitions shall not constitute a Change in Control Event: (A) any acquisition
by the Corporation or (B) any acquisition by any employee benefit plan (or
related trust) sponsored or maintained by the Corporation or any corporation
controlled by the Corporation; or

         (2) Individuals who, as of the date hereof, constitute the Board (the
"Incumbent Board") cease for any reason to constitute at least a majority of the
Board; provided, however, that any individual who becomes a director subsequent
to the date hereof whose election, or nomination for election by the
Corporation's shareholders, was approved by a vote of at least a majority of the
directors then comprising the Incumbent Board shall be considered as though such
individual were a member of the Incumbent Board; but excluding, for this
purpose, any such individual whose initial assumption of office occurs as a
result of either an actual or threatened election contest (as such terms are
used in Rule 14a-11

<PAGE>   5

of Regulation 14A promulgated under the Exchange Act) or other actual or
threatened solicitation of proxies or consents by or on behalf of a Person other
than the Board; or

         (3) Approval by the shareholders of the Corporation of a
reorganization, merger or consolidation (a "transaction"), unless, following
such transaction in each case, more than 50% of, respectively, the then
outstanding shares of common stock of the corporation resulting from such
transaction and the combined voting power of the then outstanding voting
securities of such corporation entitled to vote generally in the election of
directors is then beneficially owned, directly or indirectly, by all or
substantially all of the individuals or entities who were the beneficial owners,
respectively, of the outstanding Common Stock and Outstanding Voting Securities
immediately prior to such transaction; or

         (4) Approval by the shareholders of the Corporation of (A) a complete
liquidation or dissolution of the Corporation or (B) the sale or other
disposition of all or substantially all of the assets of the Corporation, unless
such assets are sold to a corporation and following such sale or other
disposition, the condition described in paragraph (3) above is satisfied.

         IN WITNESS WHEREOF, the Company has caused this Warrant to be executed
by its duly authorized officers, and the corporate seal hereunto affixed.

DATED: May 21, 2001                    NTN COMMUNICATIONS, INC.

                                       By:    /s/ James B. Frakes
                                          -------------------------------
                                              James B. Frakes
                                              Chief Financial Officer

                                       By:    /s/ Kathy Miles
                                          -------------------------------
                                              Kathy Miles
                                              Assistant Secretary

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