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Business Combinations (Details) - USD ($) $ in Thousands |  | 12 Months Ended
--- | --- | ---
Jul. 26, 2021 | Sep. 30, 2022 | Oct. 01, 2021 | Oct. 02, 2020
Business Combinations [Abstract] |  |  |  |
Business Combination, Acquisition Related Costs |  | $ 40,700 |  |
Payments to Acquire Businesses, Gross |  | 0 | $ 2,751,000 | $ 0
Goodwill |  | 2,176,700 | 2,176,700 |
Acquired Finite-Lived Intangible Assets [Line Items] |  |  |  |
Goodwill |  | 2,176,700 | 2,176,700 |
Payments to Acquire Businesses, Gross |  | 0 | 2,751,000 | $ 0
Business Acquisition, Pro Forma Revenue |  | 5,440,000 | 3,735,400 |
Business Acquisition, Pro Forma Net Income (Loss) |  | $ 1,514,300 | $ 637,800 |
Silicon Labs Industrial and Automotive Business |  |  |  |
Business Combinations [Abstract] |  |  |  |
Payments to Acquire Businesses, Gross | $ 2,750,000 |  |  |
Business Combination, Consideration Transferred, Equity Interests Issued and Issuable | 4,100 |  |  |
Consideration transferred | 2,754,100 |  |  |
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Inventory | 56,300 |  |  |
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Property, Plant, and Equipment | 4,400 |  |  |
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Other Noncurrent Assets | 700 |  |  |
Identifiable intangible assets | 1,708,300 |  |  |
Goodwill | 986,200 |  |  |
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Liabilities | (1,800) |  |  |
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net | 2,754,100 |  |  |
Acquired Finite-Lived Intangible Assets [Line Items] |  |  |  |
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Finite-Lived Intangibles | 1,117,200 |  |  |
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Indefinite-Lived Intangible Assets | 591,100 |  |  |
Identifiable intangible assets | 1,708,300 |  |  |
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Inventory | 56,300 |  |  |
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Property, Plant, and Equipment | 4,400 |  |  |
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Other Noncurrent Assets | 700 |  |  |
Goodwill | 986,200 |  |  |
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Liabilities | 1,800 |  |  |
Business Combination, Recognized Identifiable Assets Acquired, Goodwill, and Liabilities Assumed, Net | 2,754,100 |  |  |
Payments to Acquire Businesses, Gross | 2,750,000 |  |  |
Business Combination, Consideration Transferred, Equity Interests Issued and Issuable | 4,100 |  |  |
Consideration transferred | $ 2,754,100 |  |  |
Developed Technology and Other [Member] |  |  |  |
Acquired Finite-Lived Intangible Assets [Line Items] |  |  |  |
Useful life | 4 years |  |  |
Developed Technology and Other [Member] | Silicon Labs Industrial and Automotive Business |  |  |  |
Acquired Finite-Lived Intangible Assets [Line Items] |  |  |  |
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Finite-Lived Intangibles | $ 960,100 |  |  |
Order or Production Backlog |  |  |  |
Acquired Finite-Lived Intangible Assets [Line Items] |  |  |  |
Useful life | 2 years |  |  |
Order or Production Backlog | Silicon Labs Industrial and Automotive Business |  |  |  |
Acquired Finite-Lived Intangible Assets [Line Items] |  |  |  |
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Finite-Lived Intangibles | $ 154,600 |  |  |
Other Intangible Assets | Silicon Labs Industrial and Automotive Business |  |  |  |
Acquired Finite-Lived Intangible Assets [Line Items] |  |  |  |
Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Finite-Lived Intangibles | $ 2,500 |  |  |

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