Stockholders' Equity, Comprehensive Income and Share-Based Compensation (Effect of Share-based Compensation) (Details) - USD ($) $ in Millions	12 Months Ended
	Oct. 29, 2017	Oct. 30, 2016	Oct. 25, 2015
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	$ 220	$ 201	$ 187
Cost of products sold
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	69	62	57
Research, development, and engineering
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	83	76	69
Marketing and selling
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	28	26	26
General and administrative
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	$ 40	$ 37	$ 35