Income Taxes (Details) - USD ($) $ in Millions	12 Months Ended
	Oct. 25, 2015	Oct. 26, 2014	Oct. 27, 2013
Components of income from operations before income taxes
U.S.	$ 629	$ 612	$ 194
Foreign	969	836	156
Income before income taxes	1,598	1,448	350
Current:
U.S.	134	270	3
Foreign	199	97	72
State	18	27	2
Total current provision for income taxes	351	394	77
Deferred:
U.S.	(194)	(9)	34
Foreign	69	(3)	(19)
State	(5)	(6)	2
Total deferred provision (benefit) for income taxes	(130)	(18)	17
Provision for income taxes	$ 221	$ 376	$ 94
Reconciliation between the statutory U.S.federal income tax rate to actual effective income tax rate
Tax provision at U.S. statutory rate	35.00%	35.00%	35.00%
Resolutions from prior years’ income tax filings	(4.90%)	2.00%	(4.70%)
Effect of foreign operations taxed at various rates	(16.30%)	(10.90%)	(21.10%)
State income taxes, net of federal benefit	0.90%	1.00%	0.80%
Research and other tax credits	(0.20%)	(0.30%)	(5.40%)
U.S. domestic production deduction	(0.60%)	(1.30%)	(1.00%)
Acquisition costs	(1.10%)	0.80%	0.00%
Goodwill impairment	0.00%	0.00%	22.50%
Share-based compensation	0.80%	0.40%	2.20%
Other	0.20%	(0.70%)	(1.40%)
Effective income tax rate	13.80%	26.00%	26.90%
Deferred tax assets:
Allowance for doubtful accounts	$ 20	$ 26
Inventory reserves and basis difference	155	128
Installation and warranty reserves	11	18
Accrued liabilities	106	123
Deferred revenue	17	32
Tax credits and net operating losses	196	160
Deferred compensation	79	44
Share-based compensation	53	57
Fixed assets	0	16
Other	150	27
Gross deferred tax assets	787	631
Valuation allowance	(207)	(173)
Total deferred tax assets	580	458
Deferred tax liabilities:
Fixed assets	(15)	0
Intangible assets	(91)	(92)
Undistributed foreign earnings	(68)	(87)
Foreign exchange	(4)	(12)
Total gross deferred tax liabilities	(178)	(191)
Net deferred tax assets	402	267
Breakdown between current and non-current net deferred tax assets and liabilities
Current deferred tax asset	403	232
Non-current deferred tax asset	55	67
Non-current deferred tax liability	(56)	(32)
Net deferred tax assets	402	267
Reconciliation of gross unrecognized tax benefits
Beginning balance of gross unrecognized tax benefits	134	194	$ 174
Settlements with tax authorities	(16)	(143)	(15)
Lapses of statutes of limitation	(1)	(2)	(15)
Increases in tax positions for current year	43	52	48
Increases in tax positions for prior years	21	42	2
Decreases in tax positions for prior years	(4)	(9)	0
Ending balance of gross unrecognized tax benefits	$ 177	$ 134	$ 194