{"id":"xor-shift-produces-all-ones","text":"For any integer with alternating bits, `n ^ (n >> 1)` produces a value of the form `2^k - 1` (all ones), which is the invariant the solution checks.","truth_value":"IN","source":"entries/2026/06/06/binary-number-with-alternating-bits-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"xor-shift-produces-all-ones","truth_value":"IN","reason":"premise"}]}}