Stockholders' Equity, Comprehensive Income and Share-Based Compensation (Share-Based Compensation) (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Jul. 31, 2016	Jul. 26, 2015	Jul. 31, 2016	Jul. 26, 2015
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	$ 48	$ 46	$ 150	$ 141
Cost of products sold [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	14	14	46	43
Research, development, and engineering [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	18	17	56	52
Marketing and selling [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	7	6	20	19
General and administrative [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	$ 9	$ 9	$ 28	$ 27