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Stock-Based Compensation (Textual) (Details) - USD ($)
$ / shares in Units, shares in Millions, $ in Millions
3 Months Ended 9 Months Ended
Jul. 29, 2017
Jul. 30, 2016
Jul. 29, 2017
Jul. 30, 2016
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Annual forfeiture rate (as percent) 4.70%   4.70%  
Total intrinsic value of options exercised $ 19.9 $ 13.0 $ 109.0 $ 26.9
Proceeds received from exercise of options 18.0 16.6 105.2 39.3
Total unrecognized compensation cost related to unvested share-based awards, before tax consideration 369.8   $ 369.8  
Weighted-average period to recognize compensation cost     1 year 329 days  
Total grant-date fair value of vested stock options $ 28.3 $ 1.7 $ 95.2 $ 59.0
Stock options        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting period 5 years      
Restricted stock units (RSUs)        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Vesting period 3 years      
Market based restricted stock minimum issued upon vesting (as percent) 0.00%   0.00%  
Market based restricted stock maximum issued upon vesting (as percent) 200.00%   200.00%  
Grant-date fair value (in dollars per share) $ 75.59   $ 79.55  
Linear Technology Corporation        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Number of shares issued (in shares)     2.8  
Grant-date fair value (in dollars per share)     $ 82.20