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Stock-based Compensation (Summary of Stock-based Compensation Expense) (Details) - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Jan. 26, 2025
Jan. 28, 2024
Jan. 26, 2025
Jan. 28, 2024
Share-Based Payment Arrangement [Abstract]        
Total pre-tax stock-based compensation expense $ 17 $ 19 $ 36 $ 36
Tax-related benefits $ 4 $ 4 $ 10 $ 6