Stockholders' Equity, Comprehensive Income and Share-Based Compensation (Share-Based Compensation) (Details) (USD $) In Millions, unless otherwise specified	3 Months Ended		6 Months Ended
	Apr. 26, 2015	Apr. 27, 2014	Apr. 26, 2015	Apr. 27, 2014
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	$ 47	$ 42	$ 95	$ 88
Cost of products sold [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	14	13	29	27
Research, development, and engineering [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	17	16	35	33
Marketing and selling [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	7	5	13	11
General and administrative [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	$ 9	$ 8	$ 18	$ 17