EXHIBIT 10.4


                              BROADCOM CORPORATION

                         NOTICE OF GRANT OF STOCK OPTION

Notice is hereby given of the following option grant (the "Option") to purchase
shares of the Common Stock of Broadcom Corporation (the "Corporation"):


                                 
      Optionee:                     Alan E. Ross
      Grant Date:                   July 30, 2003
      Vesting Commencement Date     March 1, 2004 (the month after the final
                                    installment of Optionee's stock option of
                                    250,000 shares of Common Stock granted to
                                    him on November 15, 2002 vests and becomes
                                    exercisable)
      Exercise Price:               $20.71 per share
      Number of Option Shares:      250,000
      Expiration Date:              July 29, 2013
      Type of Option:               Non-Statutory Stock Option


      Exercise Schedule: The Option shall become exercisable for fifteen
      thousand (15,000) of the Option Shares upon Optionee's completion of each
      month of Service over the seventeen (17) month period (with the last month
      for ten thousand (10,000) Option Shares) measured from the Vesting
      Commencement Date and shall become exercisable for the balance of the
      Option Shares upon Optionee's continuation in Service through the last
      business day in July 2005. Notwithstanding the foregoing, in the event
      Optionee continues in Service until such time as the Corporation hires or
      promotes another individual to replace Optionee as the Corporation's
      President and Chief Executive Officer, then the Option shall, immediately
      upon the hire or promotion date of such replacement President and Chief
      Executive Officer, vest in full and become exercisable for all of the
      Option Shares as fully vested shares. In no event shall the Option become
      exercisable for any additional Option Shares after Optionee's cessation of
      Service.

      The number of Option Shares for which the Option shall become exercisable
      on any installment vesting date specified above shall be adjusted to
      reflect any stock split, stock dividend, recapitalization or other change
      in the Corporation's outstanding shares of Class A common stock which is
      effected without the Corporation's receipt of consideration.

Optionee understands and agrees that the Option is granted subject to and in
accordance with the terms of the Broadcom Corporation 1998 Stock Incentive Plan
(the "Plan"). Optionee further agrees to be bound by the terms of the Plan and
the terms of the Option as set forth in the Stock Option Agreement attached
hereto as Exhibit A. Optionee hereby acknowledges receipt of a copy of the
official prospectus for the Plan in the form attached hereto as Exhibit B. A
copy of the Plan is available upon request made to the Corporate Secretary at
the Corporation's principal offices.

No Employment or Service Contract. Nothing in this Notice or in the attached
Stock Option Agreement or in the Plan shall confer upon Optionee any right to
continue in Service for any period of specific duration or interfere with or
otherwise restrict in any way the rights of the Corporation (or any Parent or
Subsidiary employing or retaining Optionee) or of Optionee, which rights are
hereby expressly reserved by each, to terminate Optionee's Service at any time
for any reason, with or without cause.


Attachments:  A - Stock Option Agreement; B - Plan Summary and Prospectus

                              BROADCOM CORPORATION

                         NOTICE OF GRANT OF STOCK OPTION

Definitions. All capitalized terms in this Notice shall have the meaning
assigned to them in this Notice or in the attached Stock Option Agreement.


                                       
Date:  August 12, 2003

BROADCOM CORPORATION                      /s/ Alan E. Ross
                                          -------------------------------------
                                          Optionee:  Alan E. Ross

/s/ William J. Ruehle
- ---------------------------------------   -------------------------------------
By:  William J. Ruehle
Vice President and Chief Financial Officer



Attachments:  A - Stock Option Agreement; B - Plan Summary and Prospectus

                              BROADCOM CORPORATION

                         NOTICE OF GRANT OF STOCK OPTION

Notice is hereby given of the following option grant (the "Option") to purchase
shares of the Common Stock of Broadcom Corporation (the "Corporation"):


                                 
      Optionee:                     Alan E. Ross
      Grant Date:                   January 11, 2004
      Vesting Commencement Date     January 11, 2004
      Exercise Price:               $36.78 per share
      Number of Option Shares:      250,000
      Expiration Date:              January 10, 2014
      Type of Option:               Non-Statutory Stock Option


      Exercise Schedule: The Option shall become exercisable in a series of
      forty-eight (48) successive equal monthly installments upon Optionee's
      completion of each additional month of Service over the forty-eight
      (48)-month period measured from the Vesting Commencement Date.
      Notwithstanding the foregoing, in the event Optionee continues in Service
      until such time as the Corporation hires or promotes another individual to
      replace Optionee as the Corporation's President and Chief Executive
      Officer, then the Option shall, immediately upon the hire or promotion
      date of such replacement President and Chief Executive Officer, vest in
      full and become exercisable for all of the Option Shares as fully vested
      shares. In no event shall the Option become exercisable for any additional
      Option Shares after Optionee's cessation of Service.

      The number of Option Shares for which the Option shall become exercisable
      on any installment vesting date specified above shall be adjusted to
      reflect any stock split, stock dividend, recapitalization or other change
      in the Corporation's outstanding shares of Class A common stock which is
      effected without the Corporation's receipt of consideration.

Optionee understands and agrees that the Option is granted subject to and in
accordance with the terms of the Broadcom Corporation 1998 Stock Incentive Plan
(the "Plan"). Optionee further agrees to be bound by the terms of the Plan and
the terms of the Option as set forth in the Stock Option Agreement attached
hereto as Exhibit A. Optionee hereby acknowledges receipt of a copy of the
official prospectus for the Plan in the form attached hereto as Exhibit B. A
copy of the Plan is available upon request made to the Corporate Secretary at
the Corporation's principal offices.

No Employment or Service Contract. Nothing in this Notice or in the attached
Stock Option Agreement or in the Plan shall confer upon Optionee any right to
continue in Service for any period of specific duration or interfere with or
otherwise restrict in any way the rights of the Corporation (or any Parent or
Subsidiary employing or retaining Optionee) or of Optionee, which rights are
hereby expressly reserved by each, to terminate Optionee's Service at any time
for any reason, with or without cause.


Attachments:  A - Stock Option Agreement; B - Plan Summary and Prospectus

Definitions. All capitalized terms in this Notice shall have the meaning
assigned to them in this Notice or in the attached Stock Option Agreement.


                                       
Date: January 14, 2004

BROADCOM CORPORATION                      /s/ Alan E. Ross
                                          -------------------------------------
                                          Optionee: Alan E. Ross

By: /s/ William J. Ruehle
    -----------------------------------   -------------------------------------
    William J. Ruehle                     Address:
    Vice President and Chief Financial
    Officer



Attachments:  A - Stock Option Agreement; B - Plan Summary and Prospectus