{"id":"xor-mask-width-matches-input","text":"The complement mask is always exactly `num.bit_length()` bits wide via `(1 << bit_length) - 1`, so the complement never introduces bits above the MSB of the input — this is what distinguishes it from a fixed-width (e.g., 32-bit) complement.","truth_value":"IN","source":"entries/2026/06/06/number-complement-solution.md","source_url":"","source_hash":"","justifications":[],"dependents":[],"metadata":{},"created_at":"","updated_at":"","reviewed_at":"","verified_at":"","retracted_at":"","explanation":{"steps":[{"node":"xor-mask-width-matches-input","truth_value":"IN","reason":"premise"}]}}