Stockholders' Equity, Comprehensive Income and Share-Based Compensation (Share-Based Compensation) (Details) - USD ($) $ in Millions	3 Months Ended
	Jan. 27, 2019	Jan. 28, 2018
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	$ 65	$ 65
Cost of products sold
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	22	22
Research, development and engineering
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	24	24
Marketing and selling
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	8	8
General and administrative
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	$ 11	$ 11