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 December 28, 2003, 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 9, 2004

/s/ T.J. Rodgers
-------------------------
T.J. Rodgers
President and Chief Executive Officer