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Stock-based Compensation (Summary of Stock-based Compensation Expense) (Details) - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Jan. 31, 2021
Jan. 26, 2020
Jan. 31, 2021
Jan. 26, 2020
Stock-based Compensation        
Total pre-tax stock-based compensation expense $ 18 $ 18 $ 34 $ 31
Tax-related benefits $ 3 3 $ 6 6
Discontinued Operations, Held-for-sale or Disposed of by Sale [Member]        
Stock-based Compensation        
Total pre-tax stock-based compensation expense   1   2
Tax-related benefits   $ 0   $ 0