Stockholders' Equity, Comprehensive Income and Share-Based Compensation (Effect of Share-based Compensation) (Details) (USD $) In Millions, unless otherwise specified	12 Months Ended
	Oct. 26, 2014	Oct. 27, 2013	Oct. 28, 2012
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	$ 177	$ 162	$ 182
Cost of products sold [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	53	50	54
Research, development, and engineering [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	66	53	54
Marketing and selling [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	23	20	22
General and administrative [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	35	34	52
Restructuring charge [Member]
Employee Service Share-based Compensation, Allocation of Recognized Period Costs [Line Items]
Total share-based compensation	$ 0	$ 5	$ 0