Stockholders' Equity, Comprehensive Income and Share-Based Compensation (Share-Based Compensation) (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	May. 01, 2016	Apr. 26, 2015	May. 01, 2016	Apr. 26, 2015
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	$ 48	$ 47	$ 102	$ 95
Cost of products sold [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	15	14	32	29
Research, development, and engineering [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	18	17	38	35
Marketing and selling [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	6	7	13	13
General and administrative [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	$ 9	$ 9	$ 19	$ 18