<PAGE>   1
                                                                   EXHIBIT 10.43

        THIS WARRANT AND THE SECURITIES ISSUABLE UPON THE EXERCISE HEREOF HAVE
        NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933. THEY MAY NOT BE
        SOLD, OFFERED FOR SALE, PLEDGED, HYPOTHECATED, OR OTHERWISE TRANSFERRED
        EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER THE
        SECURITIES ACT OF 1933, OR AN OPINION OF COUNSEL SATISFACTORY TO THE
        COMPANY THAT REGISTRATION IS NOT REQUIRED UNDER SUCH ACT OR UNLESS SOLD
        PURSUANT TO RULE 144 UNDER SUCH ACT.



                     WARRANT NO. 2 TO PURCHASE COMMON STOCK
                                       OF
                        DIGITAL GENERATION SYSTEMS, INC.

                           VOID AFTER DECEMBER 9, 2003



               This Warrant is issued to Scott K. Ginsburg, or his registered
assigns ("Holder") by Digital Generation Systems, Inc., a California corporation
(the "Company"), on December 9, 1998 (the "Warrant Issue Date").

               1. Purchase Shares. Subject to the terms and conditions
hereinafter set forth, the Holder is entitled, upon surrender of this Warrant at
the principal office of the Company (or at such other place as the Company shall
notify the holder hereof in writing), to purchase from the Company up to one
million five hundred forty-eight thousand four hundred sixty (1,548,460) fully
paid and nonassessable shares of Common Stock of the Company, as constituted on
the Warrant Issue Date (the "Common Stock"). The number of shares of Common
Stock issuable pursuant to this Section 1 (the "Shares") shall be subject to
adjustment pursuant to Section 10 hereof.

               2. Exercise Price. The purchase price for the Shares shall be
$3.25, as adjusted from time to time pursuant to Section 10 hereof (the
"Exercise Price").

               3. Exercise Period. This Warrant shall not be exercisable prior
to December 9, 1999. Thereafter, this Warrant shall be exercisable as follows:

                  (a) This Warrant shall be exercisable only with respect to
that portion of Shares that have vested (the "Vested Shares"), subject to the
other restrictions in this Section 3. The Shares shall vest in equal monthly
installments upon the Holder's completion of each of the twenty-four (24) months
of continuous Service measured from and after the Warrant Issue Date.

<PAGE>   2

                  (b) In the event that the Company is subject to a Change in
Control on or after June 9, 1999, all of the Shares that have not yet vested
shall immediately vest and become Vested Shares.

                  (c) This Warrant shall be exercisable for up to seven hundred
seventy-four thousand two hundred thirty (774,230) of the Vested Shares, in
whole or in part with respect to such Vested Shares, during the term commencing
on the date that the closing price of the Company's Common Stock on the Nasdaq
National Market has exceeded $10.00 per share for at least twenty (20) of the
preceding thirty (30) consecutive trading days and ending on 5:00 p.m. on
December 9, 2003. This Warrant shall not be exercisable, at any time, with
respect to any of the Shares that are not Vested Shares.

                  (d) This Warrant shall become exercisable with respect to all
of the Vested Shares, in whole or in part, during the term commencing on the
date that the closing price of the Company's Common Stock on the Nasdaq National
Market has exceeded $15.00 per share for at least twenty (20) of the preceding
thirty (30) consecutive trading days and ending on 5:00 p.m. on December 9,
2003. This Warrant shall not be exercisable, at any time, with respect to any of
the Shares that are not Vested Shares.

                  (e) Notwithstanding paragraphs (a), (b), (c) and (d) of this
Section 3, in the event that the Holder has provided continuous Service to the
Company from the Warrant Issue Date through November 8, 2003 (the "End Vesting
Date"), this Warrant shall become exercisable with respect to all of the Shares
as of the End Vesting Date.

               4. Representations and Warranties of the Company. The Company
hereby represents and warrants to the Holder that:

                  (a) Authorization. All corporate action on the part of the
Company, its officers, directors and stockholders necessary for the
authorization, execution and delivery of this Warrant and that certain
Registration Rights Agreement of even date herewith, by and between the Company
and certain investors (the "Registration Rights Agreement"), the performance of
all obligations of the Company hereunder and thereunder, and the authorization,
issuance (or reservation for issuance), and delivery of this Warrant and the
Shares issuable upon conversion of this Warrant has been taken or will be taken
prior to the date hereof, and this Warrant and the Registration Rights Agreement
constitute valid and legally binding obligations of the Company, enforceable in
accordance with its terms, except (i) as limited by applicable bankruptcy,
insolvency, reorganization, moratorium, and other laws of general application
affecting enforcement of creditors' rights generally, (ii) as limited by laws
relating to the availability of specific performance, injunctive relief, or
other equitable remedies, and (iii) to the extent the indemnification provisions
contained in the Registration Rights Agreement may be limited by applicable
federal or state securities laws.

                  (b) Valid Issuance. This Warrant, when issued, sold and
delivered in accordance with the terms set forth herein and in consideration for
the Service provided by the Holder, will be duly and validly issued, fully paid,
and nonassessable, and will be free of restrictions on transfer other than
restrictions on transfer under this Warrant and the Registration


                                       2
<PAGE>   3

Rights Agreement and under applicable state and federal securities laws. The
Shares issuable upon conversion of this Warrant have been duly and validly
reserved for issuance and, upon issuance in accordance with the terms of the
Company's Amended and Restated Articles of Incorporation, will be duly and
validly issued, fully paid, and nonassessable and will be free of restrictions
on transfer other than restrictions on transfer under this Warrant and the
Registration Rights Agreement and under applicable state and federal securities
laws. The Company agrees that, prior to the expiration of this Warrant, the
Company will at all time have authorized and reserved, and will keep available,
solely for issuance or delivery upon the exercise of this Warrant, the number of
shares of Common Stock as from time to time shall be issuable upon the exercise
of this Warrant.

                  (c) Offering. Subject in part to the truth and accuracy of the
Holder's representations set forth in Section 5 of this Warrant, the offer, sale
and issuance of this Warrant is exempt from the registration requirements of any
applicable state and federal securities laws, and neither the Company nor any
authorized agent acting on its behalf will take any action hereafter that would
cause the loss of such exemption.

                  (d) Non-Contravention. To the best of the Company's knowledge,
the execution and delivery of this Warrant, the issuance of the Shares to be
issued by the Company upon conversion of this Warrant, and the consummation of
the transactions contemplated hereby will not conflict with or constitute a
violation of, or default (with the passage of time or otherwise) under, any
material agreement or instrument to which the Company is a party or by which it
is bound or the Articles of Incorporation (the "Charter") or the Bylaws of the
Company nor result in the creation or imposition of any lien, encumbrance,
claim, security interest or restriction whatsoever upon any of the material
properties or assets of the Company or an acceleration of indebtedness pursuant
to any obligation, agreement or condition contained in any material bond,
debenture, note or any other evidence of indebtedness or any material indenture,
mortgage, deed of trust or any either agreement or instrument to which the
Company is a party or by which the Company is bound or to which any of the
property or assets of the Company is subject, nor conflict with, or result in a
violation of, any law, administrative regulation, ordinance or order of any
court or governmental agency, arbitration panel or authority applicable to the
Company. No consent, approval, authorization or other order of, or registration,
qualification or filing with, any regulatory body, administrative agency, or
other governmental body in the United States, other than with respect to "blue
sky" laws, is required for the valid issuance of this Warrant or the Shares to
be issued upon conversion of this Warrant (other than such as have been made or
obtained).

                  (e) Capitalization. All documents that the Company was
required to file under the Securities Exchange Act of 1934, as amended (the
"Exchange Act"), during the twelve (12) months preceding the date of this
Warrant (the "SEC Filings") accurately reflected the capitalization of the
Company as of their respective filing or effective dates, as the case may be.
The Shares and the shares of Common Stock issuable upon conversion of that
certain Warrant No. 1 to Purchase Common Stock of even date herewith issued to
the Holder (together, the "Combined Shares") represent greater than fifty
percent (50%) of the sum of (a) the Combined Shares and (b) the number of shares
of Common Stock of the Company issuable upon


                                       3
<PAGE>   4

exercise of those warrants issued pursuant to that certain Common Stock and
Warrant Purchase Agreement of even date herewith, by and among the Company and
certain investors.

                  (f) Legal Proceedings. Except as disclosed in the SEC Filings,
there is no material legal or governmental proceeding pending or, to the
knowledge of the Company, threatened or contemplated to which the Company is or
may be a party or of which the business or property of the Company is or may be
subject.

                  (g) No Violations. Except as disclosed in the SEC Filings, the
Company is not in violation of its Charter or Bylaws, in violation of any law,
administrative regulation, ordinance or order of any court or governmental
agency, arbitration panel or authority applicable to the Company, which
violation, individually or in the aggregate, would have a material adverse
effect on the business or financial condition of the Company, or in default in
any material respect in the performance of any obligation, agreement or
condition contained in any bond, debenture, note or any other evidence of
indebtedness in any indenture, mortgage, deed of trust or any other agreement or
instrument to which the Company is a party or by which the Company is bound or
by which the properties of the Company are bound or affected, which default,
individually or in the aggregate, would have a material adverse effect on the
business or financial condition of the Company or which would have otherwise
have a material adverse effect on the Holder, and there exists no condition
which, with the passage of time or the giving of notice or both, would
constitute a material default under any such document or instrument or result in
the imposition of any material penalty or the acceleration of any indebtedness.

                  (h) Governmental Permits, Etc. Except as disclosed in the SEC
Filings, the Company has all necessary franchises, licenses, certificates and
other authorizations from any foreign, federal, state or local government or
governmental agency, department, or body that are currently necessary for the
operation of the business of the Company as currently conducted, the absence of
which would have a material adverse effect on the business or operations of the
Company.

                  (i) Financial Statements. Except as disclosed in the SEC
Filings, the financial statements of the Company and the related notes contained
in the Company's Annual Report on Form 10-K for the fiscal year ended December
31, 1997 and its Quarterly Report on Form 10-Q for the quarter ended September
30, 1998, present fairly the financial position of the Company as of the dates
indicated therein and its results of operations and cash flows for the periods
therein specified. Such financial statements (including the related notes) have
been prepared in accordance with generally accepted accounting principles
applied on a consistent basis throughout the periods therein specified.

                  (j) No Material Adverse Charge. Except as disclosed in the SEC
Filings, since September 30, 1998, there has not been any material adverse
change in its business, financial condition or results of operations.

                  (k) Additional Information. The Company has filed in a timely
manner all SEC Filings. The SEC Filings complied in all material respects with
the requirements of the Exchange Act or the Securities Act of 1933, as amended
(the "Securities Act"), as the case


                                       4
<PAGE>   5

may be, as of their respective filing or effective dates, and the information
contained therein was true and correct in all material respects as of the date
or effective date of such documents, and each of the SEC Filings, as of such
date, did not contain an untrue statement of material fact or omit to state a
material fact required to be stated therein or necessary to make the statements
therein, in light of the circumstances under which they were made, not
misleading.

               (l) Intellectual Property. Except to the extent that the failure
to comply with any of the following statements would not have a material adverse
effect on the business or operations of the Company, the Company hereby
represents and warrants that as of the date hereof:

                   (1) the Company has the right to use all intellectual
property (the "Intellectual Property") now used by it in its business;

                   (2) the Company owns all right, title and interest in and to,
all of the intellectual property it owns, free and clear of any liens or
encumbrances;

                   (3) in any case in which the Company does not own
Intellectual Property, it has good and valid licenses for the same which are in
full force and effect; and

                   (4) no claims have been asserted with respect to the use of
any such Intellectual Property or challenging or questioning the validity or
effectiveness of any such license or agreement.

               (m) Listing. The Company shall use its best efforts to comply
with all requirements of the National Association of Securities Dealers, Inc.
with respect to the issuance of the Shares and the listing of the Shares on the
Nasdaq National Market.

               5. Representations and Warranties of the Holder. The Holder
hereby represents and warrants that:

                  (a) Authorization. Such Holder has full power and authority to
acknowledge and enter into this Warrant and the Registration Rights Agreement,
and this Warrant and the Registration Rights Agreement constitute valid and
legally binding obligation, enforceable in accordance with its terms except (i)
as limited by applicable bankruptcy, insolvency, reorganization, moratorium, and
other laws of general application affecting enforcement of creditors' rights
generally, (ii) as limited by laws relating to the availability of specific
performance, injunctive relief, or other equitable remedies, and (iii) to the
extent the indemnification provisions contained in the Registration Rights
Agreement may be limited by applicable federal or state securities laws.

                  (b) Purchase Entirely for Own Account. This Warrant is issued
to such Holder in reliance upon such Holder's representation to the Company,
which by such Holder's acknowledgement of this Warrant such Holder hereby
confirms, that this Warrant and the Shares issuable upon exercise of this
Warrant to be received by such Holder (collectively, the


                                       5
<PAGE>   6

"Securities") will be acquired for investment for such Holder's own account, not
as a nominee or agent, and not with a view to the resale or distribution of any
part thereof, and that such Holder has no present intention of selling, granting
any participation in, or otherwise distributing the same. By acknowledging this
Warrant, such Holder further represents that such Holder does not have any
contract, undertaking, agreement or arrangement with any person to sell,
transfer or grant participations to such person or to any third person, with
respect to any of the Securities.

                  (c) Investment Experience. Such Holder is an investor in
securities of companies in the development stage and acknowledges that it is
able to fend for itself, can bear the economic risk of its investment, and has
such knowledge and experience in financial or business matters that it is
capable of evaluating the merits and risks of the investment in this Warrant. If
other than an individual, Holder also represents it has not been organized for
the purpose of acquiring this Warrant.

                  (d) Accredited Investor. Such Holder is an "accredited
investor" within the meaning of Securities and Exchange Commission ("SEC") Rule
501 of Regulation D, as presently in effect.

                  (e) Restricted Securities. Such Holder understands that the
Securities it is being issued are characterized as "restricted securities" under
the federal securities laws inasmuch as they are being acquired from the Company
in a transaction not involving a public offering and that under such laws and
applicable regulations such securities may be resold without registration under
the Act, only in certain limited circumstances. In this connection, such Holder
represents that it is familiar with SEC Rule 144, as presently in effect, and
understands the resale limitations imposed thereby and by the Act.

                  (f) Further Limitations on Disposition. Without in any way
limiting the representations set forth above, such Holder further agrees not to
make any disposition of all or any portion of the Securities unless and until
the transferee has agreed in writing for the benefit of the Company to be bound
by this Section 5 and the Registration Rights Agreement provided and to the
extent this Section 5 and such agreement are then applicable, and:

                      (1) There is then in effect a Registration Statement under
the Securities Act of 1933, as amended, covering such proposed disposition and
such disposition is made in accordance with such Registration Statement; or

                      (2) (i) Such Holder shall have notified the Company of the
proposed disposition and shall have furnished the Company with a detailed
statement of the circumstances surrounding the proposed disposition, and (ii) if
reasonably requested by the Company, such Holder shall have furnished the
Company with an opinion of counsel, reasonably satisfactory to the Company that
such disposition will not require registration of such shares under the Act. It
is agreed that the Company will not require opinions of counsel for transactions
made pursuant to SEC Rule 144 except in unusual circumstances.

                      (3) Notwithstanding the provisions of Paragraphs (a) and
(b) above, no such registration statement or opinion of counsel shall be
necessary for a transfer by


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<PAGE>   7

the Holder that is a partnership to a partner of such partnership or a retired
partner of such partnership who retires after the date hereof, or to the estate
of any such partner or retired partner or the transfer by gift, will or
intestate succession of any partner to his or her spouse or to the siblings,
lineal descendants or ancestors of such partner or his or her spouse, if the
transferee agrees in writing to be subject to the terms hereof to the same
extent as if he or she were an original Holder hereunder.

                  (g) Legends. It is understood that the certificates evidencing
the Securities may bear one or all of the following legends:

                      (1) "These securities have not been registered under the
Securities Act of 1933, as amended. They may not be sold, offered for sale,
pledged or hypothecated in the absence of a registration statement in effect
with respect to the securities under such Act or an opinion of counsel
satisfactory to the Company that such registration is not required or unless
sold pursuant to Rule 144 of such Act."

                      (2) Any legend required by the laws of the State of
California, including any legend required by the California Department of
Corporations and Sections 417 and 418 of the California Corporations Code.

                      (3) Any legend required by applicable blue sky law.

               6. Method of Exercise. While this Warrant remains outstanding and
exercisable in accordance with Section 3 above, the Holder may exercise, in
whole or in part, the purchase rights evidenced hereby. Such exercise shall be
effected by:

                  (a) the surrender of the Warrant, together with a duly
executed copy of the form of Notice of Election attached hereto, to the
Secretary of the Company at its principal offices; and

                  (b) the payment to the Company of an amount equal to the
aggregate Exercise Price for the number of Shares being purchased.

               7. Assumption of Warrant. If at any time, while this Warrant, or
any portion thereof, is outstanding and unexpired there shall be (i) an
acquisition of the Company by another entity by means of a merger,
consolidation, or other transaction or series of related transactions resulting
in the exchange of the outstanding shares of the Company's Capital Stock such
that shareholders of the Company prior to such transaction own, directly or
indirectly, less than 50% of the voting power of the surviving entity, or (ii) a
sale or transfer of all or substantially all of the Company's assets to any
other person, then, as a part of such acquisition, sale or transfer, lawful
provision shall be made so that the Holder shall thereafter be entitled to
receive upon exercise of this Warrant, during the period specified herein and
upon payment of the Exercise Price then in effect, the number of shares of stock
or other securities or property of the successor corporation resulting from such
acquisition, sale or transfer which a holder of the shares deliverable upon
exercise of this Warrant would have been entitled to receive in such
acquisition, sale or transfer if this Warrant had been exercised immediately
before such acquisition, sale or


                                       7
<PAGE>   8

transfer, all subject to further adjustment as provided in this Section 7; and,
in any such case, appropriate adjustment (as determined by the Company's Board
of Directors) shall be made in the application of the provisions herein set
forth with respect to the rights and interests thereafter of the Holder to the
end that the provisions set forth herein (including provisions with respect to
changes in and other adjustments of the number of Warrant Shares of the Holder
is entitled to purchase) shall thereafter by applicable, as nearly as possible,
in relation to any shares of Common Stock or other securities or other property
thereafter deliverable upon the exercise of this Warrant.

               8. Certificates for Shares. Upon the exercise of the purchase
rights evidenced by this Warrant, one or more certificates for the number of
Shares so purchased shall be issued as soon as practicable thereafter (with
appropriate restrictive legends, if applicable), and in any event within thirty
(30) days of the delivery of the subscription notice.

               9. Issuance of Shares. The Company covenants that the Shares,
when issued pursuant to the exercise of this Warrant, will be duly and validly
issued, fully paid and nonassessable and free from all taxes, liens, and charges
with respect to the issuance thereof.

               10. Adjustment of Exercise Price and Number of Shares. The number
of and kind of securities purchasable upon exercise of this Warrant and the
Exercise Price shall be subject to adjustment from time to time as follows:

                   (a) Subdivisions, Combinations and Other Issuances. If the
Company shall at any time prior to the expiration of this Warrant subdivide its
Common Stock, by split-up or otherwise, or combine its Common Stock, or issue
additional shares of its Common Stock or Common Stock as a dividend with respect
to any shares of its Common Stock, the number of Shares issuable on the exercise
of this Warrant shall forthwith be proportionately increased in the case of a
subdivision or stock dividend, or proportionately decreased in the case of a
combination. Appropriate adjustments shall also be made to the purchase price
payable per share, but the aggregate purchase price payable for the total number
of Shares purchasable under this Warrant (as adjusted) shall remain the same.
Any adjustment under this Section 10(a) shall become effective at the close of
business on the date the subdivision or combination becomes effective, or as of
the record date of such dividend, or in the event that no record date is fixed,
upon the making of such dividend.

                   (b) Reclassification, Reorganization and Consolidation. In
case of any reclassification, capital reorganization, or change in the Common
Stock of the Company (other than as a result of a subdivision, combination, or
stock dividend provided for in Section 10(a) above), then, as a condition of
such reclassification, reorganization, or change, lawful provision shall be
made, and duly executed documents evidencing the same from the Company or its
successor shall be delivered to the Holder, so that the Holder shall have the
right at any time prior to the expiration of this Warrant to purchase, at a
total price equal to that payable upon the exercise of this Warrant, the kind
and amount of shares of stock and other securities and property receivable in
connection with such reclassification, reorganization, or change by a holder of
the same number of shares of Common Stock as were purchasable by the Holder
immediately prior


                                       8
<PAGE>   9

to such reclassification, reorganization, or change. In any such case
appropriate provisions shall be made with respect to the rights and interest of
the Holder so that the provisions hereof shall thereafter be applicable with
respect to any shares of stock or other securities and property deliverable upon
exercise hereof, and appropriate adjustments shall be made to the purchase price
per share payable hereunder, provided the aggregate purchase price shall remain
the same.

                   (c) Notice of Adjustment. When any adjustment is required to
be made in the number or kind of shares purchasable upon exercise of the
Warrant, or in the Exercise Price, the Company shall promptly notify the holder
of such event and of the number of shares of Common Stock or other securities or
property thereafter purchasable upon exercise of this Warrant.

               11. Withholding Taxes. In the event that the Company determines
that it is required to withhold any tax as a result of the exercise of this
Warrant, the Holder, as a condition to the exercise of this Warrant, shall make
arrangements satisfactory to the Company to enable it to satisfy all withholding
requirements. The Holder shall also make arrangements satisfactory to the
Company to enable it to satisfy any withholding requirements that may arise in
connection with the vesting or disposition of Shares purchased by exercising
this Warrant.

               12. No Fractional Shares or Scrip. No fractional shares or scrip
representing fractional shares shall be issued upon the exercise of this
Warrant, but in lieu of such fractional shares the Company shall make a cash
payment therefor on the basis of the Exercise Price then in effect.

               13. No Shareholder Rights. Prior to exercise of this Warrant, the
Holder shall not be entitled to any rights of a shareholder with respect to the
Shares, including (without limitation) the right to vote such Shares, receive
dividends or other distributions thereon, exercise preemptive rights or be
notified of shareholder meetings, and such holder shall not be entitled to any
notice or other communication concerning the business or affairs of the Company.
However, nothing in this Section 13 shall limit the right of the Holder to be
provided the Notices required under this Warrant.

               14. Transfers of Warrant. Subject to compliance with applicable
federal and state securities laws, this Warrant and all rights hereunder are
transferable in whole or in part by the Holder to any person or entity upon
written notice to the Company. The transfer shall be recorded on the books of
the Company upon the surrender of this Warrant, properly endorsed, to the
Company at its principal offices, and the payment to the Company of all transfer
taxes and other governmental charges imposed on such transfer. In the event of a
partial transfer, the Company shall issue to the holders one or more appropriate
new warrants.

               15. Successors and Assigns. The terms and provisions of this
Warrant shall inure to the benefit of, and be binding upon, the Company and the
Holders hereof and their respective successors and assigns.

               16. Amendments and Waivers. Any term of this Warrant may be
amended and the observance of any term of this Warrant may be waived (either
generally or in a particular


                                       9
<PAGE>   10

instance and either retroactively or prospectively), with the written consent of
the Company and the Holder.

               17. Notices. All notices required under this Warrant and shall be
deemed to have been given or made for all purposes (i) upon personal delivery,
(ii) upon confirmation receipt that the communication was successfully sent to
the applicable number if sent by facsimile; (iii) one day after being sent, when
sent by professional overnight courier service, or (iv) five days after posting
when sent by registered or certified mail. Notices to the Company shall be sent
to the principal office of the Company (or at such other place as the Company
shall notify the Holder hereof in writing). Notices to the Holder shall be sent
to the address of the Holder on the books of the Company (or at such other place
as the Holder shall notify the Company hereof in writing).

               18. Attorneys' Fees. If any action of law or equity is necessary
to enforce or interpret the terms of this Warrant, the prevailing party shall be
entitled to its reasonable attorneys' fees, costs and disbursements in addition
to any other relief to which it may be entitled.

               19. Captions. The section and subsection headings of this Warrant
are inserted for convenience only and shall not constitute a part of this
Warrant in construing or interpreting any provision hereof.

               20. Governing Law. This Warrant shall be governed by the laws of
the State of California as applied to agreements among California residents made
and to be performed entirely within the State of California.

               21. Definitions.

                   (a) "Board of Directors" shall mean the Board of Directors of
the Company, as constituted from time to time or, if a Committee has been
appointed, such Committee.

                   (b) "Change in Control" shall mean:

                       (1) The consummation of a merger or consolidation of the
Company with or into another entity or any other corporate reorganization, if
persons who were not shareholders of the Company immediately prior to such
merger, consolidation or other reorganization own immediately after such merger,
consolidation or other reorganization 50% or more of the voting power of the
outstanding securities of each of (A) the continuing or surviving entity and (B)
any direct or indirect parent corporation of such continuing or surviving
entity; or

                       (2) The sale, transfer or other disposition of all or
substantially all of the Company's assets.

A transaction shall not constitute a Change in Control if its sole purpose is to
change the state of the Company's incorporation or to create a holding company
that will be owned in substantially


                                       10
<PAGE>   11

the same proportions by the persons who held the Company's securities
immediately before such transaction.

                   (c) "Code" shall mean the Internal Revenue Code of 1986, as
amended.

                   (d) "Company" shall mean Digital Generation Systems, Inc., a
California corporation.

                   (e) "Consultant" shall mean an individual who performs bona
fide services for the Company, a Parent or a Subsidiary as a consultant or
advisor, excluding Employees and Outside Directors.

                   (f) "Employee" shall mean any individual who is a common-law
employee of the Company, a Parent or a Subsidiary.

                   (g) "Fair Market Value" shall mean the fair market value of a
Share, as determined by the Board of Directors in good faith. Such determination
shall be conclusive and binding on all persons.

                   (h) "Outside Director" shall mean a member of the Board of
Directors who is not an Employee.

                   (i) "Outside Director" shall mean a member of the Board of
Directors who is not an Employee.

                   (j) "Parent" shall mean any corporation (other than the
Company) in an unbroken chain of corporations ending with the Company, if each
of the corporations other than the Company owns stock possessing 50% or more of
the total combined voting power of all classes of stock in one of the other
corporations in such chain.

                   (k) "Securities Act" shall mean the Securities Act of 1933,
as amended.

                   (l) "Service" shall mean service as an Employee, Outside
Director or Consultant.

                   (m) "Subsidiary" shall mean any corporation (other than the
Company) in an unbroken chain of corporations beginning with the Company, if
each of the corporations other than the last corporation in the unbroken chain
owns stock possessing 50% or more of the total combined voting power of all
classes of stock in one of the other corporations in such chain.

                   (n) "Warrant" shall mean this Warrant.


                                       11
<PAGE>   12



               IN WITNESS WHEREOF, Digital Generation Systems, Inc. caused this
Warrant to be executed by an officer thereunto duly authorized.



                                          DIGITAL GENERATION SYSTEMS, INC.



                                       By:
                                          ------------------------------------
                                          Henry W. Donaldson,
                                          President and Chief Executive Officer





ACKNOWLEDGED AND AGREED:


By:                                 
   -------------------------------
   Scott K. Ginsburg





            SIGNATURE PAGE TO WARRANT NO. 2 TO PURCHASE COMMON STOCK
                       OF DIGITAL GENERATION SYSTEMS, INC.

<PAGE>   13

                               NOTICE OF EXERCISE



To:  DIGITAL GENERATION SYSTEMS, INC.

               The undersigned hereby elects to purchase _________________
shares of Common Stock of Digital Generation Systems, Inc., pursuant to the
terms of the attached Warrant and payment of the Exercise Price per share
required under such Warrant accompanies this notice.

               The undersigned hereby represents and warrants that the
undersigned is acquiring such shares for its own account for investment purposes
only, and not for resale or with a view to distribution of such shares or any
part thereof.

                                            WARRANTHOLDER:



                                         By:                                  
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                                            Scott K. Ginsburg

                             Address:                                        
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Date:                        
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Name in which shares should be registered:

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