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Stock-Based Compensation and Shareholders' Equity - Textual (Details) - USD ($)
12 Months Ended
Aug. 21, 2018
Nov. 03, 2018
Oct. 28, 2017
Oct. 29, 2016
Oct. 28, 2006
Aug. 31, 2004
Stock-Based Compensation (Textuals) [Abstract]            
Shares reserved for future issuance   25,500,000.0        
Units/Awards granted (USD per share)   $ 87.88        
Minimum maturity of traded options used to estimate volatility   1 year        
Annual forfeiture rate   5.00%        
Total intrinsic value of options exercised   $ 123,800,000 $ 144,600,000 $ 46,600,000    
Proceeds (cash) received from exercise of options   99,000,000 133,300,000 61,500,000    
Total unrecognized compensation cost related to unvested share-based awards, before tax consideration   $ 350,700,000        
Weighted-average period for recognition of compensation cost in years   1 year 233 days        
Total grant-date fair value of vested stock options   $ 136,100,000 $ 114,800,000 $ 62,800,000    
Preferred stock, shares authorized (in shares)   471,934   471,934    
Preferred stock, par value (USD per share)   $ 1   $ 1    
Preferred stock, shares outstanding (in shares)   0   0    
Preferred stock, shares issued (in share)   0        
Employee Stock Option [Member]            
Stock-Based Compensation (Textuals) [Abstract]            
Vesting period (years)   4 years 5 years      
Percentage of awards exercisable in annual installments on each of the first, second, third, fourth and fifth anniversaries   25.00% 20.00%      
Maximum contractual term of all option   10 years        
Restricted Stock Units (RSUs) [Member]            
Stock-Based Compensation (Textuals) [Abstract]            
Vesting period (years)   4 years        
Percentage of awards exercisable in annual installments on each of the first, second, third, fourth and fifth anniversaries   25.00%        
2006 Stock Incentive Plan [Member]            
Stock-Based Compensation (Textuals) [Abstract]            
Maximum common stock granted (in shares)         34,000,000  
Total number of common shares available for future grantUnits/Awards granted (in shares)   11,400,000.0        
2010 Stock Plan Incentive [Member]            
Stock-Based Compensation (Textuals) [Abstract]            
Total number of common shares available for future grantUnits/Awards granted (in shares)   1,600,000        
Common Stock Repurchase Program [Member]            
Stock-Based Compensation (Textuals) [Abstract]            
Amount authorized to repurchase company common stock           $ 8,200,000,000.0
Number of additional shares authorized, value 2,000,000,000.0          
Repurchased common stock, shares (in shares)   148,900,000        
Repurchased common stock, value   $ 5,600,000,000        
Repurchase of common stock   $ 2,600,000,000.0        
Linear Technology Corporation [Member]            
Stock-Based Compensation (Textuals) [Abstract]            
Number of share issued (shares)   2,800,000        
Units/Awards granted (USD per share)   $ 82.20        
Accounting Standards Update 2016-09 [Member]            
Stock-Based Compensation (Textuals) [Abstract]            
Adjustments to additional paid in capital, income tax benefit from share-based compensation   $ 26,200,000