EXHIBIT 5.1

October 9, 2007

Board of Directors

National Semiconductor Corporation

2900 Semiconductor Drive

Santa Clara, California 95051

Gentlemen:

At your request, I have examined the registration statement on Form S-8 (the “Registration Statement”) which you are filing with the United States Securities and Exchange Commission pursuant to the Securities Act of 1933, as amended, for registration of 14,000,000 shares of Common Stock, par value $0.50 per share (the “Shares”) of National Semiconductor Corporation (the “Company”) to be issued under the Company’s 2007 Employees Equity Plan (the “EEP”) and 3,000,000 Shares of Common Stock to be issued under the Company’s 2005 Executive Officer Equity Plan (the “EOEP”).

In connection with this opinion, I have examined the EEP, the EOEP, the Company’s Certificate of Incorporation and By-Laws, as amended, and such other documents and records as deemed necessary as a basis for this opinion.

Based on the foregoing, I am of the opinion that the Shares, when issued in accordance with each applicable plan, the Registration Statement and related final prospectus, and applicable state laws, will be legally issued, fully paid and nonassessable.

I consent to the filing of this opinion as an Exhibit to the Registration Statement.

Very truly yours,

//s// NANCY LUCKE LUDGUS

NANCY LUCKE LUDGUS

Associate General Counsel &

Assistant Secretary