BINDING MEMORANDUM OF UNDERSTANDING

Exhibit 10.36

BINDING MEMORANDUM OF UNDERSTANDING

This BINDING MEMORANDUM OF UNDERSTANDING, dated this 5th day of January, 2007 (“MOU”), states the terms of a binding agreement between John F. (“Jack”) Gifford (“Gifford”) and Maxim Integrated Products, Inc. (“Maxim”).

1. This MOU is entered into with reference to the following facts:

a. On December 8, 2006, Gifford notified Tunc Doluca, a Maxim group president, that he was seriously considering retirement based on the advice of his treating physician and his disability. On December 15, 2006, Gifford notified the Board of Directors of Maxim that his treating physician had advised him that he is “disabled” as that term is defined in the Amended and Restated Employment Agreement (“1994 Employment Agreement”) and Gifford proposed that, on the advice of his treating physician, he would voluntarily retire from his employment as Chairman, CEO, President, and member of the Board of Directors of Maxim, effective December 31, 2006, and that he and the Company enter into a Retirement Agreement to address the issues related to his disability and the 1994 Employment Agreement.

b. Gifford has notified the Board of Directors of Maxim, pursuant to section 9.1 of the 1994 Employment Agreement between Gifford and Maxim, that he is willing and able to continue to be employed by Maxim on a part-time basis as a consultant to Maxim advising on matters of Maxim’s choosing;

c. Maxim has agreed to waive the 120-day termination-notice requirement contained in section 9 of the 1994 Employment Agreement; and,

d. Maxim and Gifford have agreed to enter into a retirement agreement that will include each of the terms set forth below. (“Retirement Agreement”) This MOU fully supersedes and replaces the 1994 Employment Agreement until the Retirement Agreement is signed, at which time the Retirement Agreement will supercede and replace this MOU.

2. Termination Notice: Gifford hereby retires from his positions as Chief Executive Officer, President, and Chairman of the Board of Directors effective December 31, 2006. Gifford also hereby retires from his position as a member of the Board of Directors of Maxim. Maxim waives any requirement of 120 days advance written notice by Gifford in Section 9 of 1994 Employment Agreement.

3. Employment Status: Gifford will be employed by Maxim on a part-time basis (i.e., up to a maximum of 24 hours a week) as a consultant to Maxim, advising on matters of the company’s choosing, including, for example, product planning and direction, and business unit management.

4. Termination of Part-Time Employment: Maxim may terminate Gifford’s part-time employment with or without “cause.” For purposes of this MOU and the Retirement Agreement, “cause” shall mean (i) fraud or other illegal act; (ii) dishonesty against Maxim; or (iii) habitual drunkenness or drug dependency affecting Gifford’s performance of the duties of his

employment. Gifford may voluntarily terminate his part-time employment for “good reason” or for no reason. For purposes of this MOU and the Retirement Agreement, “good reason” shall exist if (1) Maxim materially diminishes Gifford’s responsibilities related to his part-time employment, (2) Maxim requires that Gifford relocate his residence as a condition of continuing his part-time employment with Maxim, (3) Maxim materially breaches any of the provisions of this MOU, or (4) Gifford is determined by a qualified physician (to be mutually agreed upon by Gifford and Maxim, which agreement shall not be unreasonably withheld) to be disabled by accident, or sickness, or otherwise so as to render him mentally or physically incapable of performing the services required of him as described in paragraph 3 of this MOU for a period of at least ninety (90) consecutive days. Gifford will not be entitled to terminate for good reason based on disability for 90 days from the date of execution of this MOU. If Maxim terminates Gifford’s part-time employment without “cause” or Gifford terminates his part-time employment for “good reason,” Gifford shall be entitled to a one-time lump-sum payment of $300,000.

5. Compensation: $300,000.00 annually, based upon full-time employment and payable in proportion to hours worked (i.e., 20 hours a week for an entire year equates to $150,000 in compensation).

6. Vesting: During such period as Gifford remains employed by Maxim, his Maxim stock options and shares of restricted Maxim stock shall remain outstanding and shall vest at a rate equal to a percentage of their former vesting rate, which percentage shall be determined by dividing by 65 the number of days worked by Gifford in the relevant quarter. With respect to the stock options and restricted stock that did not vest but would have vested had Gifford remained employed full-time, they will not be cancelled, but will remain outstanding (respectively, “remaining non-qualified stock options” and “remaining restricted stock units”). The vesting schedule for the remaining non-qualified stock options will be revised so that each will be scheduled to vest in the equivalent fiscal quarter of the first fiscal year in which Gifford has no non-qualified stock options scheduled to vest and will vest according to the percentage calculation set forth above (i.e., if fiscal year 2011 is the first fiscal year in which Gifford has no options scheduled to vest, non-qualified stock options remaining after a vesting calculation performed in Q3 ‘07 will be rescheduled to vest in Q3 ‘11; options remaining after a vesting calculation performed in Q4 ‘07 will be rescheduled to vest in Q4 ‘11, and so forth). Similarly, the vesting schedule for the remaining restricted stock units will be revised so that each will be scheduled to vest in the equivalent fiscal quarter of the first fiscal year in which Gifford has no restricted stock units scheduled to vest and will vest according to the percentage calculation set forth above. Each year, prior to the anniversary of this MOU, Maxim’s Board of Directors will meet to evaluate Gifford’s relative contribution to the success of Maxim during the preceding year and will grant to Gifford such new options as it deems appropriate. Should Maxim terminate Gifford’s part-time employment without “cause” (as defined above) or should Gifford resign for “good reason” (as defined above), all of Gifford’s then-outstanding stock options and restricted stock units shall immediately and fully vest.

7. Health and Other Insurance Coverage: Gifford and his wife shall be entitled to Maxim health insurance coverage for the remainder of each of their lives, consistent with the definition of “coverage” set forth in Section 9.2 of the 1994 Employment Agreement, regardless of the reason for the termination of Gifford’s part-time employment, or the expiration of the

Retirement Agreement. While Gifford remains employed by Maxim on a part-time basis, Maxim shall continue to provide coverage to Gifford under Maxim’s then-existing life and disability insurance policies applicable to Maxim’s officers, consistent with the coverage currently being provided to Gifford so long as those terms are consistent with Maxim’s insurance policies. While Gifford remains employed by Maxim on a part-time basis, Maxim shall continue to provide coverage to Gifford under Maxim’s then-existing personal liability insurance policies applicable to Maxim’s chief executive officer, consistent with the coverage currently being provided to Gifford so long as those terms are consistent with Maxim’s insurance policies. Following the termination of Gifford’s employment with Maxim, Maxim shall continue to provide to Gifford coverage under Maxim’s then-existing life and disability insurance policies applicable to retired officers of Maxim, consistent with the coverage provided to other retired Maxim officers, the terms of those insurance policies and applicable law. Following the termination of Gifford’s employment with Maxim, Maxim shall continue to provide to Gifford coverage under Maxim’s then-existing personal liability insurance policies applicable to the chief executive officer of Maxim, consistent with the coverage provided to Maxim’s chief executive officer, the terms of those insurance policies and applicable law. With respect to all of the insurance described in this paragraph 7, Gifford shall be required to pay the same amount for such insurance coverage as a full-time Maxim officer would be required to pay for such coverage under the applicable Maxim plan and/or policy.

8. Bonus: Gifford will no longer be eligible for the Maxim officer or employee bonus program after December 31, 2007. Gifford will, however, be eligible for one half of the fiscal year 2007 bonus based on the bonus plan that currently applies to the CEO and officers of Maxim.

9. Indemnity Agreement: This MOU and the Retirement Agreement shall effect no change to the existing indemnity agreement between Gifford and Maxim.

10. D&O Insurance Policy: Maxim will provide Gifford with all such “tail coverage” as is available to the CEO and the Board of Directors.

11. Deferred Compensation: The Board will approve, with Gifford’s consent, the further acceleration of the distribution of Gifford’s vested account balance under his Deferred Compensation Agreement at December 31, 2004 on or before January 31, 2007 (less amounts already distributed on September 21, 2006 and to be distributed on December 28, 2006). In addition, the Board will approve, with Gifford’s consent, the acceleration of the distribution of his vested account balance for amounts deferred in 2005 and 2006 on January 24, 2008 to be paid in a lump sum; provided, however, that such amount will be distributed earlier in a lump sum in the event of Gifford’s death or his retirement from part-time employment with Maxim.

12. Office and Assistant: Maxim will provide Gifford with the same office that Gifford is utilizing now and Candy Flett (formerly Candy Beers) will continue to be his administrative assistant throughout the period he remains as a part-time employee. If Gifford’s part-time employment terminates through his retirement or termination by Maxim without “cause,” Maxim will continue to provide his existing office space and Candy Flett as his administrative assistant provided he remains available to consult to Maxim. Candy Flett will be provided as Gifford’s

administrative assistant pursuant to this Section 12 to the extent she remains employed by Maxim, and is willing to do so; provided that if Ms. Flett is not available for these reasons, Maxim will assign another administrative assistant acceptable to Gifford to work with Gifford pursuant to this Section 12. If Gifford’s part-time employment terminates through his retirement or termination by Maxim without “cause” and Gifford is not providing services to Maxim, Maxim may, in lieu of providing Gifford with his current office, provide Gifford with office space comparable to his current office space and located not on a Maxim campus but within a reasonable distance from Gifford’s residence, along with an administrative assistant acceptable to Gifford. If Gifford’s employment is terminated for “cause” (as defined above), Gifford shall not be entitled to the above-referenced office space and assistant.

13. Competitive Activity. During the period while Gifford is receiving salary from Maxim as a part-time employee, receiving insurance coverage from Maxim pursuant to paragraph 7, above, or receiving benefits pursuant to paragraph 12, above, Gifford will not directly engage in activities for, nor render services to, any firm or business organization which directly competes with Maxim in any line of business then engaged in by Maxim.

14. This Memorandum of Understanding is fully binding upon the parties and all successors and assigns. Gifford and Maxim agree to subsequently enter into a mutually agreeable Retirement Agreement, which shall include each of the terms set forth in this MOU. This MOU fully supersedes and replaces the 1994 Employment Agreement until the Retirement Agreement is signed, at which time the Retirement Agreement will supercede and replace this MOU. Gifford’s and Maxim’s rights and responsibilities under the 1994 Employment Agreement will, therefore, be extinguished.

IN WITNESS WHEREOF, this MOU has been signed by or on behalf of each of the parties as of the day first above written. The parties hereto agree that this MOU may be executed in counterparts.