Acquisitions (Details) $ / shares in Units, shares in Millions			12 Months Ended			15 Months Ended
		Jul. 22, 2014 USD ($) $ / shares	Oct. 29, 2016 USD ($) segment $ / shares shares	Oct. 31, 2015 USD ($) $ / shares	Nov. 01, 2014 USD ($) shares	Oct. 31, 2015 USD ($) $ / shares	Jul. 26, 2016 USD ($) $ / shares
Business Acquisition [Line Items]
Business Acquisition, Equity Interest Issued or Issuable, Number of Shares | shares			0.7		0.7
Grant date fair value of restricted stock units issued in connection with Acquisition | $ / shares		$ 48.20
Business Combination, Acquired Receivables, Gross Contractual Amount		$ 37,300,000
Business Combination, Acquired Receivables, Estimated Uncollectible		300,000
Number of reportable segments | segment			1
Number of operating segments | segment			7
Short-term Debt		$ 2,000,000,000
Common Stock, Par or Stated Value Per Share | $ / shares		$ 0.01	$ 0.166	$ 0.166		$ 0.166
Business Acquisition, Share Price | $ / shares		$ 78.00
Initial cash payments		$ 2,400,000,000
Business Acquisition Contingent Consideration Cash Payment	[1]		$ 1,489,000	$ 2,000,000
BusinessAcquisitionPurchasePriceAllocationIntangibleAssetsNotAmortizable1		900,000
Payments to Acquire Businesses, Net of Cash Acquired			83,170,000	7,065,000	$ 1,945,887,000
Developed technology			$ 718,365,000	677,264,000		$ 677,264,000
Acquisition related costs				9,700,000	$ 41,200,000	$ 50,900,000
Linear Technology Corporation [Member]
Business Acquisition [Line Items]
Business Acquisition, Equity Interest Issued or Issuable, Number of Shares | shares			58.0
Fair value of the consideration transferred totaled			$ 14,800,000,000
Business Acquisition, Share Price | $ / shares							$ 46.00
BusinessCombinationEquityInterestsIssuedandIssuableConversionRatioperShare			0.2321
Acquisition related costs			12,200,000
Expected Long Term Financing related to acquisition							$ 11,600,000,000
Business Combination Termination Rights Fee If Closing Conditions Are Not Satisfied			700,000,000
Hittite Microwave Corporation [Member]
Business Acquisition [Line Items]
Business Acquisition, Effective Date of Acquisition					Jul. 22, 2014
Fair value of replacement share-based awards		6,541,000
Accounts receivable		36,991,000
Intangible assets		666,400,000
Fair value of the consideration transferred totaled		2,424,446,000			$ 2,400,000,000
Short-term Debt		2,000,000,000
Initial cash payments		2,430,987,000
Goodwill acquired			$ 0
Deferred tax assets		2,242,000
Deferred tax liabilities		$ 276,683,000
Selling, Marketing, General and Administrative Expense [Member]
Business Acquisition [Line Items]
Acquisition related costs				$ 9,700,000	33,300,000
Nonoperating Income (Expense) [Member]
Business Acquisition [Line Items]
Acquisition related costs					$ 7,900,000

[1] Recorded in research and development expense in the consolidated statements of income.