Exhibit 32.1



                           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 Annual Report of National Semiconductor  Corporation (the
"Company")  on Form 10-K for the  period  ended May 28,  2006 as filed  with the
Securities and Exchange  Commission on the date hereof (the "Report"),  I, Brian
L. Halla,  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: July 24, 2006                               \s\ Brian L. Halla
                                                  -----------------------
                                                   Brian L. Halla
                                                   Chief Executive Officer





                           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 Annual Report of National Semiconductor  Corporation (the
"Company")  on Form 10-K for the  period  ended May 28,  2006 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.


Date: July 24, 2006                         \s\ Lewis Chew
                                            -----------------------
                                            Lewis Chew
                                            Senior Vice President, Finance and
                                            Chief Financial Officer