Stockholders' Equity, Comprehensive Income and Share-Based Compensation (Share-Based Compensation) (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Apr. 29, 2018	Apr. 30, 2017	Apr. 29, 2018	Apr. 30, 2017
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	$ 64	$ 53	$ 129	$ 107
Cost of products sold
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	21	16	43	33
Research, development and engineering
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	24	21	48	41
Marketing and selling
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	8	7	16	14
General and administrative
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	$ 11	$ 9	$ 22	$ 19