WARRANT TO PURCHASE SHARES OF COMMON STOCK OF MATHSTAR, INC.

Exhibit 10.19

THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR APPLICABLE STATE SECURITIES LAWS AND MAY NOT BE SOLD, TRANSFERRED, ASSIGNED, OFFERED, PLEDGED OR OTHERWISE DISTRIBUTED FOR VALUE UNLESS THERE IS AN EFFECTIVE REGISTRATION STATEMENT UNDER SUCH ACT AND SUCH LAWS COVERING SUCH SECURITIES OR MATHSTAR, INC. (THE “COMPANY”) RECEIVES AN OPINION OF COUNSEL ACCEPTABLE TO THE COMPANY STATING THAT SUCH SALE, TRANSFER, ASSIGNMENT, OFFER, PLEDGE OR OTHER DISTRIBUTION FOR VALUE IS EXEMPT FROM THE REGISTRATION AND PROSPECTUS DELIVERY REQUIREMENTS OF SUCH ACT AND SUCH LAWS.

WARRANT

TO PURCHASE               SHARES OF COMMON STOCK

OF

MATHSTAR, INC.

THIS CERTIFIES THAT, for good and valuable consideration,                                              , or                     registered assigns (the “Holder”), is entitled to subscribe for and purchase from MathStar, Inc., a Minnesota corporation (the “Company”), on or before 5:00 p.m. Minneapolis, Minnesota time on                    , 200     (the “Expiration Date”),                              (               ) fully paid and nonassessable shares of the Common Stock of the Company at an exercise price per share equal to eighty percent (80%) of the Price to Public in the initial public offering of the Company’s Common Stock (the “IPO”) which is effective on or before the maturity date (as such maturity date may be extended) of the first promissory notes (the “Notes”) issued in the offering (the “Offering”) described in the Company’s Confidential Private Placement Memorandum dated March 4, 2005 of which the sale of this Warrant is a part.  If the IPO is not effective before such maturity date, the exercise price shall be $1.60 per share (the “Warrant Exercise Price”), subject to adjustment as provided in this Warrant.  This Warrant shall become exercisable upon the earlier of the effective date of the IPO or upon the maturity date of the first Notes issued in the Offering (including any extension of their term).  The number of shares of Common Stock which may be acquired upon exercise of this Warrant, as they may be adjusted from time to time, are referred to herein as the “Warrant Shares.”  As used herein, the term “Common Stock” means and includes the Company’s presently authorized common stock, $0.01 par value per share, and shall also include any capital stock of any class of the Company hereafter authorized which shall not be limited to a fixed sum or percentage in respect of the rights of the holders thereof to participate in dividends or in the distribution of assets upon the voluntary or involuntary liquidation, dissolution, or winding up of the Company.  This Warrant is one of the series of Warrants substantially identical in form which may be issued by the Company from time to time to purchase shares of Common Stock designated as “No. BR -                ,” and the term “Warrants” as used herein means all of such Warrants (including this Warrant).

This Warrant is subject to the following provisions, terms and conditions:

1.                                       Exercise:  Transferability.

(a)                                  Subject to the provisions of Section 3 hereof, the rights represented by this Warrant may be exercised by the Holder hereof, in whole or in part (but not as to a fractional share of Common Stock), by written notice of exercise (in the form attached hereto) delivered to the Company at the principal office of the Company before the Expiration Date and accompanied or preceded by the surrender of this Warrant along with cash, wire transfer, or a certified or bank check in payment of the Warrant Exercise Price for the total number of Warrant Shares then being purchased.  In the sole discretion of the Company, the total Warrant Exercise Price may be paid by personal check.

2.                                       Exchange and Replacement.  Subject to Sections 1 and 7 hereof, this Warrant is exchangeable upon the surrender hereof by the Holder to the Company at its office for new Warrants of like tenor and date representing in the aggregate the right to purchase the number of Warrant Shares purchasable hereunder, each of such new Warrants to represent the right to purchase such number of Warrant Shares (not to exceed the aggregate total number purchasable hereunder) as shall be designated by the Holder at the time of such surrender.  Upon receipt by the Company of evidence reasonably satisfactory to it of the loss, theft, destruction, or mutilation of this Warrant and, in case of loss, theft or destruction, of indemnity or security reasonably satisfactory to it, and upon surrender and cancellation of this Warrant, if mutilated, the Company will make and deliver a new Warrant of like tenor, in lieu of this Warrant.  This Warrant shall be promptly canceled by the Company upon the surrender hereof in connection with any exchange or replacement.  The Company shall pay any and all expenses, taxes (other than stock transfer taxes), and other charges payable in connection with the preparation, execution, and delivery of Warrants pursuant to this Section 2.

3.                                       Issuance of the Warrant Shares.

(a)                                  The Company agrees that the Warrant Shares purchased hereunder shall be and are deemed to be issued to the Holder as of the close of business on the date on which this Warrant shall have been surrendered and the payment made for such Warrant Shares as aforesaid.  Subject to the provisions of Section 3(b), stock certificates for the Warrant Shares so purchased shall be delivered to the Holder within a reasonable time, not exceeding fifteen (15) days after the date on which the rights represented by this Warrant shall have been so exercised if the Warrant Exercise Price has been paid with cash, wire transfer or a certified or bank check, or twenty (20) days after such date if the Warrant Exercise Price has been paid with a personal check.  Unless this Warrant has expired, a new Warrant representing the right to purchase the number of Warrant Shares, if any, with respect to which this Warrant shall not then have been exercised shall also be delivered to the Holder within such times.

(b)                                 Notwithstanding the foregoing, the Company shall not be required to deliver any stock certificate for Warrant Shares upon exercise of this Warrant except in accordance with exemptions from the applicable securities registration requirements or registrations under

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applicable securities laws.  Upon any proposed transfer or other disposition of this Warrant or the Warrant Shares, the  Holder thereof shall provide the Company with written representations from the Holder and the proposed transferee in form and substance satisfactory to the Company regarding the transfer or, at the election of the Company, an opinion of counsel reasonably satisfactory to the Company to the effect that the proposed transfer or disposition of this Warrant or the Warrant Shares may be effected without registration or qualification (under any federal or applicable state or other applicable securities laws) of this Warrant or the Warrant Shares.  Upon receipt by the Company of such written notice and either such representations or opinion, such Holder shall be entitled to transfer this Warrant, or to exercise this Warrant in accordance with its terms, or to dispose of the Warrant Shares, all in accordance with the terms of the notice delivered by such Holder to the Company, provided that an appropriate legend, if any, respecting the aforesaid restrictions on transfer and disposition may be endorsed on this Warrant or the stock certificates for the Warrant Shares.  The Holder agrees to execute such documents and make such representations, warranties, and agreements as may be required to comply with the exemption relied upon by the Company, or the registration made, for the exercise of this Warrant or issuance or transfer of the Warrant or the Warrant Shares.

4.                                       Covenants of the Company.  The Company covenants and agrees that upon the proper exercise of this Warrant by the Holder, all Warrant Shares will, upon issuance, be duly authorized and issued, fully paid, nonassessable, and free from all taxes, liens, and charges with respect to the issue thereof except for any taxes, liens and charges imposed on or with respect to the property of the Holder.  The Company further covenants and agrees that during the period within which the rights represented by this Warrant may be exercised, the Company will at all times have authorized and reserved for the purpose of issue or transfer upon exercise of the rights evidenced by this Warrant a sufficient number of shares of Common Stock to provide for the exercise of the rights represented by this Warrant.

5.                                       Adjustments.  The provisions of this Warrant are subject to adjustment as provided in this Section 5.

(a)                                  The Warrant Exercise Price shall be adjusted from time to time such that if the Company shall hereafter:

(i)                                     pay any dividends on the Common Stock payable in Common Stock or securities convertible into Common Stock;

(ii)                                  subdivide its then outstanding shares of Common Stock into a greater number of shares; or

(iii)                               combine outstanding shares of Common Stock by reverse stock split, reclassification or otherwise;

then, in any such event, the Warrant Exercise Price in effect immediately before such event shall (until adjusted again pursuant hereto) be adjusted immediately after such event to a price (calculated to the nearest full cent) determined by dividing (i) the number of shares of Common Stock outstanding immediately before such event, multiplied by the then existing Warrant

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Exercise Price, by (ii) the total number of shares of Common Stock outstanding immediately after such event, and the resulting quotient shall be the adjusted per share Warrant Exercise Price.  An adjustment made pursuant to this Section 5(a) shall become effective immediately after the record date in the case of a dividend or distribution and immediately after the effective date in the case of a subdivision, combination or reclassification.  If, as a result of an adjustment made pursuant to this Section 5(a), the Holder of any Warrant thereafter surrendered for exercise shall become entitled to receive shares of two or more classes of capital stock or shares of Common Stock and other capital stock of the Company, the Company’s board of directors (whose determination shall be conclusive) shall determine the allocation of the adjusted Warrant Exercise Price between or among shares of such classes of capital stock or shares of Common Stock and other capital stock.  If, as a result of an adjustment made pursuant to this Section 5(a), the Holder of any Warrant thereafter surrendered for exercise shall become entitled to receive any shares of the Company other than shares of Common Stock, thereafter the Warrant Exercise Price of such other shares so receivable upon exercise of any Warrant shall be subject to adjustment from time to time in a manner and on terms as nearly equivalent as practicable to the provisions with respect to Common Stock contained in this Section 5.

(b)                                 Upon each adjustment of the Warrant Exercise Price pursuant to Section 5(a) above, the Holder of each Warrant shall thereafter (until another such adjustment) be entitled to purchase at the adjusted Warrant Exercise Price the number of shares, calculated to the nearest full share, obtained by multiplying the number of shares specified in such Warrant (as adjusted as a result of all adjustments in the Warrant Exercise Price in effect before such adjustment) by the Warrant Exercise Price in effect before such adjustment and dividing the product so obtained by the adjusted Warrant Exercise Price.

(c)                                  Upon any consolidation or merger to which the Company is a party, other than a merger or consolidation in which the Company is the continuing corporation, or upon any sale or conveyance to another corporation of the property of the Company as an entirety or substantially as an entirety, or upon any statutory exchange of securities by the Company with another corporation (including any exchange effected in connection with a merger of a third corporation into the Company), there shall be no adjustment under Section 5(a), but instead the Holder of each Warrant then outstanding shall have the right thereafter to convert such Warrant into the kind and amount of shares of stock and other securities and property which such Holder would have owned or have been entitled to receive immediately after such consolidation, merger, statutory exchange, sale, or conveyance had such Warrant been converted immediately before the effective date of such consolidation, merger, statutory exchange, sale, or conveyance and, in any such case, if necessary, appropriate adjustment shall be made in the application of the provisions set forth in this Section 5 with respect to the rights and interests thereafter of any Holders of the Warrant so that the provisions set forth in this Section 5 shall thereafter correspondingly be made applicable, as nearly as may reasonably be, in relation to any shares of stock and other securities and property thereafter deliverable on the exercise of the Warrant.  The provisions of this Section 5(c) shall similarly apply to successive consolidations, mergers, statutory exchanges, sales or conveyances.

(d)                                 Upon any adjustment of the Warrant Exercise Price, then and in each such case, the Company shall within ten (10) days after the date when the circumstances giving rise to the

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adjustment occurred give written notice thereof, by first-class mail, postage prepaid, addressed to the Holder as shown on the books of the Company, which notice shall state the Warrant Exercise Price resulting from such adjustment and the increase or decrease, if any, in the number of shares of Common Stock purchasable at such price upon the exercise of this Warrant, setting forth in reasonable detail the method of calculation and the facts upon which such calculation is based.

6.                                       No Shareholder Rights.  This Warrant shall not entitle the Holder to any voting rights or other rights as a shareholder of the Company, and the Holder of this Warrant shall not be deemed to be a shareholder of the Company for any purpose whatsoever with respect to the shares subject to this Warrant except with respect to the shares of Common Stock for which this Warrant has been duly exercised by the Holder.

7.                                       Notice of Transfer of Warrant or Resale of the Warrant Shares.

(a)                                  Subject to the sale, assignment, hypothecation, or other transfer restrictions set forth in Section 1 hereof, the Holder, by acceptance hereof, agrees to give written notice to the Company before transferring this Warrant or transferring any Warrant Shares of such Holder’s intention to do so, describing briefly the manner of any proposed transfer.  Promptly upon receiving such written notice, the Company shall present copies thereof to the Company’s counsel.  If, in the opinion of such counsel, the proposed transfer may be effected without registration or qualification under any federal or state or other applicable securities laws, the Company, as promptly as practicable, shall notify the Holder of such opinion, whereupon the Holder shall be entitled to transfer this Warrant or to dispose of Warrant Shares received upon the previous exercise of this Warrant, all in accordance with the terms of the notice delivered by the Holder to the Company; provided that an appropriate legend may be endorsed on this Warrant or the certificates for such Warrant Shares respecting restrictions upon transfer thereof necessary or advisable in the opinion of counsel to the Company and satisfactory to the Company to prevent further transfers which would be in violation of Section 5 of the Securities Act of 1933, as amended (the “1933 Act”), and applicable state or other applicable securities laws; and provided further that the Holder and prospective transferee or purchaser shall execute such documents and make such representations, warranties, and agreements as may be required solely to comply with the exemptions relied upon by the Company for the transfer or disposition of the Warrant or Warrant Shares.

(b)                                 If, in the opinion of counsel to the Company, the proposed transfer or disposition of this Warrant or such Warrant Shares described in the written notice given pursuant to this Section 7 may not be effected without registration or qualification of this Warrant or such Warrant Shares, the Company shall promptly give written notice thereof to the Holder, and the Holder will limit its activities in respect to such as, in the opinion of such counsel, are permitted by law.

8.                                       Fractional Shares.

(a)                                  Fractional shares shall not be issued upon the exercise of this Warrant, but in any case where the Holder would, except for the provisions of this Section, be entitled under the terms hereof to receive a fractional share, the Company shall, upon the exercise of this Warrant

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for the largest number of whole shares then called for, pay a sum in cash equal to the sum of (i) the excess, if any, of the Fair Market Value (as defined in Section 8(b)) of such fractional share over the proportional part of the Warrant Exercise Price represented by such fractional share, plus (ii) the proportional part of the Warrant Exercise Price represented by such fractional share.

(b)                                 Fair Market Value of a share of Common Stock as of a particular date (the “Determination Date”) shall mean:

(i)                                     If the Company’s Common Stock is traded on an exchange or is quoted on The NASDAQ National Market, then the average closing or last sale prices, respectively, reported for the ten (10) consecutive trading days immediately preceding the Determination Date;

(ii)                                  If the Company’s Common Stock is not traded on an exchange or on The NASDAQ National Market but is traded on The NASDAQ SmallCap Market or other over-the-counter market, then the average closing bid and asked prices reported for the ten (10) consecutive trading days immediately preceding the Determination Date; and

(iii)                               If the Company’s Common Stock is not traded on an exchange or on The NASDAQ National Market or The NASDAQ SmallCap Market or other over-the-counter market, then the price established in good faith by the Company’s Board of Directors.

9.                                       Miscellaneous.

(a)                                  Whenever reference is made herein to the issue or sale of shares of Common Stock, the term “Common Stock” shall include any stock of any class of the Company other than preferred stock with a fixed limit on dividends and a fixed amount payable in the event of any voluntary or involuntary liquidation, dissolution or winding up of the Company.

(b)                                 The Company will not, by amendment of its Articles of Incorporation or through reorganization, consolidation, merger, dissolution or sale of assets, or by any other voluntary act or deed, avoid or seek to avoid the observance or performance of any of the covenants, stipulations or conditions to be observed or performed hereunder by the Company, but will, at all times in good faith, assist, insofar as it is able, in the carrying out of all provisions hereof and in the taking of all other action which may be necessary in order to protect the rights of the Holder hereof against dilution.  The Company’s amendment of its Articles of Incorporation solely to effect a reverse stock split shall not be deemed an amendment, act or deed described in the foregoing sentence.

(c)                                  Upon written request of the Holder of this Warrant, the Company will promptly provide such holder with a then current written list of the names and addresses of all Holders of warrants originally issued under the terms of, and concurrent with, this Warrant.

(d)                                 The representations, warranties and agreements herein contained shall survive the exercise of this Warrant.  References to the “holder of” include the immediate holder of shares

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purchased on the exercise of this Warrant, and the word “holder” shall include the plural thereof.  This Common Stock Purchase Warrant shall be interpreted under the laws of the State of Minnesota, without regard to its conflict of law provisions.

(e)                                  All shares of Common Stock or other securities issued upon the exercise of the Warrant shall be validly issued, fully paid and non-assessable.

(f)                                    Neither this Warrant nor any term hereof may be changed, waived, discharged or terminated orally but only by an instrument in writing signed by the Company and the Holder.

IN WITNESS WHEREOF, MathStar, Inc. has caused this Warrant to be signed by its duly authorized officer and this Warrant to be dated                         , 2005.

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TO:                            MATHSTAR, INC.

The undersigned hereby irrevocably elects to exercise the attached Warrant to purchase for cash,                                 of the shares issuable upon the exercise of such Warrant, and requests that stock certificates for such shares (together with a new Warrant to purchase the number of shares, if any, with respect to which this Warrant is not exercised) shall be issued in the name of

*The signature on the Notice of Exercise of Warrant must correspond to the name as written upon the face of the Warrant in every particular without alteration or any change whatsoever.  When signing on behalf of a corporation, partnership, trust or other entity, please indicate your position(s) and title(s) with such entity.  If the Warrant is registered in the name of more than one Holder, all Holders must sign.

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ASSIGNMENT FORM

To be signed only upon authorized transfer of Warrants.

FOR VALUE RECEIVED, the undersigned hereby sells, assigns, and transfers unto                                                              the right to purchase the securities of MathStar, Inc. to which the within Warrant relates and appoints                                             , attorney, to transfer said right on the books of MathStar, Inc. with full power of substitution in the premises.