Exhibit 32


                            CERTIFICATION PURSUANT TO
                  18 U.S.C SECTION 1350, AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002



In connection with the Quarterly  Report of National  Semiconductor  Corporation
(the  "Company")  on Form 10-Q for the period  ended  February 29, 2004 as filed
with the Securities and Exchange  Commission on the date hereof (the  "Report"),
I, Brian L.  Halla,  President  and Chief  Executive  Officer  for the  Company,
certify,  pursuant  to 18  U.S.C.  1350,  as  adopted  pursuant  to  906  of the
Sarbanes-Oxley Act of 2002, that, to my knowledge:

     (1)  The Report fully  complies with the  requirements  of Section 13(a) or
          Section 15(d), as applicable,  of the Securities Exchange Act of 1934,
          and

     (2)  The  information  contained  in the  Report  fairly  presents,  in all
          material respects,  the financial  condition and results of operations
          of the Company.



Date: April 5, 2004
                                         \s\ Brian L. Halla
                                         ------------------
                                         Brian L. Halla
                                         President and Chief Executive Officer


                                                                      Exhibit 32


                            CERTIFICATION PURSUANT TO
                  18 U.S.C SECTION 1350, AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002



In connection with the Quarterly  Report of National  Semiconductor  Corporation
(the  "Company")  on Form 10-Q for the period  ended  February 29, 2004 as filed
with the Securities and Exchange  Commission on the date hereof (the  "Report"),
I, Brian L.  Halla,  President  and Chief  Executive  Officer  for the  Company,
certify,  pursuant  to 18  U.S.C.  1350,  as  adopted  pursuant  to  906  of the
Sarbanes-Oxley Act of 2002, that, to my knowledge:

     (1)  The Report fully  complies with the  requirements  of Section 13(a) or
          Section 15(d), as applicable,  of the Securities Exchange Act of 1934,
          and

     (2)  The  information  contained  in the  Report  fairly  presents,  in all
          material respects,  the financial  condition and results of operations
          of the Company.

 Date: April 5, 2004
                                             \s\ Lewis Chew
                                             --------------
                                             Lewis Chew
                                             Senior Vice President, Finance and
                                             Chief Financial Officer