Bitwise Operations Calculator mechanism

Model scope

The truth-table concept for AND, OR, and XOR is standard, but the instrument is not fully specified for fixed-width behavior. The exact unresolved ambiguities are operand signedness, pre-operation masking, result masking, shift-count handling, rotate-count normalization, right-shift semantics, supported maximum width, decimal output convention, and the input shape for unary NOT.

• The rotate formula is incomplete: it needs masking to n bits and normalization of k, such as k = ((k mod n) + n) mod n, followed by ((x << k) | (x >>> (n - k))) & ((1 << n) - 1). As written, rotating an n-bit value by n can produce a value wider than n bits.
• The rotate formula does not state whether the right shift is logical or arithmetic; rotation requires a logical right shift over the selected width.
• NOT requires width masking, for example (~x) & ((1 << n) - 1). A raw NOT operation can produce a negative signed result rather than an n-bit complement.
• The semantics of <<, >>, and >>> at a selected bit width are unspecified, including overflow truncation, signedness, and whether operands are masked before shifting.
• The specification does not define whether decimal output is unsigned or signed two's-complement, nor how negative input integers are represented.
• The specification says two operands even though NOT is unary; the required input shape for NOT is unspecified.

Units and conventions

• Bit width n is a positive integer and is dimensionless.
• Operands and shift counts are integers; shift counts are dimensionless integers.
• For these test vectors, operands are interpreted as unsigned n-bit values and masked to 0 through 2^n - 1.
• Binary output is exactly n bits with leading zero padding; hexadecimal output is the corresponding unsigned value padded to the selected width where applicable.
• The >>> operation is interpreted as a logical right shift within the selected width.
• For rotation, k is normalized modulo n.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "operation": "AND",
    "x": 172,
    "y": 102,
    "bit_width": 8
  },
  "expected_outputs": {
    "result_bin": "00100100",
    "result_hex": "0x24",
    "result_dec": 36
  },
  "working": "172 = 10101100₂ and 102 = 01100110₂. Bit by bit: 1&0=0, 0&1=0, 1&1=1, 0&0=0, 1&0=0, 1&1=1, 0&1=0, 0&0=0. Therefore 10101100₂ AND 01100110₂ = 00100100₂ = 0x24 = 36."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

A zero-bit rotate produces an undefined negative shift count and has no valid result, so the calculator must reject it. The rotate operation also has a left-versus-right direction ambiguity unless the supplied formula and n-bit masking convention are enforced.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche2/tranche2-results.json
• BOUNDARY_HAZARD_CATALOG.json