Stockholders' Equity, Comprehensive Income and Share-Based Compensation (Effect of Share-based Compensation) (Details) - USD ($) $ in Millions	12 Months Ended
	Oct. 31, 2021	Oct. 25, 2020	Oct. 27, 2019
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	$ 346	$ 307	$ 263
Income tax benefits recognized	43	39	37
Cost of products sold
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	118	103	89
Research, development, and engineering
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	129	116	99
Marketing and selling
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	43	36	31
General and administrative
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	$ 56	$ 52	$ 44