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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 fiscal year ended May 29, 2011 as filed with the Securities and Exchange Commission on the date hereof (the "Report"), I, Donald Macleod, Chairman, President and Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 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 26, 2011 \s\ Donald Macleod
Donald Macleod
Chairman, President and
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 fiscal year ended May 29, 2011 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 of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 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 26, 2011 \s\ Lewis Chew
Lewis Chew
Senior Vice President, Finance
and Chief Financial Officer

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