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

      I, T.J. Rodgers, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that the Annual Report on Form 10-K of Cypress Semiconductor Corporation for the fiscal year ended January 2, 2005 fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and the information contained in such Annual Report on Form 10-K fairly presents, in all material respects, the financial condition and results of operations of the Cypress Semiconductor Corporation.

Dated: March 18, 2005

/s/ T.J. Rodgers

T.J. Rodgers

President and Chief Executive Officer