Stockholders' Equity, Comprehensive Income and Share-Based Compensation (Share-Based Compensation) (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Jul. 30, 2017	Jul. 31, 2016	Jul. 30, 2017	Jul. 31, 2016
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	$ 55	$ 48	$ 162	$ 150
Cost of products sold
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	18	14	51	46
Research, development, and engineering
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	20	18	61	56
Marketing and selling
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	7	7	21	20
General and administrative
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	$ 10	$ 9	$ 29	$ 28