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 August 24, 2003 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.


Dated: October 2, 2003
                                           \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 August 24, 2003 as filed with
the Securities  and Exchange  Commission on the date hereof (the  "Report"),  I,
Lewis Chew,  Senior Vice President,  Finance and Chief Financial 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.


Dated: October 2, 2003                       \s\ Lewis Chew
                                             Lewis Chew
                                             Senior Vice President, Finance and
                                             Chief Financial Officer