Stockholders' Equity, Comprehensive Income and Share-Based Compensation (Effect of Share-based Compensation) (Details) - USD ($) $ in Millions	12 Months Ended
	Oct. 25, 2015	Oct. 26, 2014	Oct. 27, 2013
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	$ 187	$ 177	$ 162
Cost of products sold
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	57	53	50
Research, development and engineering
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	69	66	53
Marketing and selling
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	26	23	20
General and administrative
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	35	35	34
Restructuring charge
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	$ 0	$ 0	$ 5