Exhibit 32(a)

Certification of Periodic Report

Pursuant to 18 U.S.C. Section 1350

For purposes of 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned, Thomas J. Engibous, the Chairman of the Board, President and Chief Executive Officer of Texas Instruments Incorporated (the “Company”), hereby certifies that, to his knowledge:

(i) the Annual Report on Form 10-K of the Company for the year ended December 31, 2003, as filed with the Securities and Exchange Commission on the date hereof (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(ii) the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: February 27, 2004

/s/    THOMAS J. ENGIBOUS        

Thomas J. Engibous

Chairman of the Board, President and Chief

Executive Officer