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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