Base Converter & Bitwise Toolkit mechanism

Model scope

The listed claims are implementable under standard conventions, but the declared interface is incomplete and several semantics are ambiguous. Add operand, operation, and shift inputs; specify radix and width constraints; define fixed-width NOT, overflow, signedness, and right-shift behavior before release.

• Positional-notation conversion is named but not formally defined; the standard formula should be value = sum(digit_i × source_base^i), with digit validity and integer-input constraints.
• Bitwise operations require a second operand, but the declared inputs list only number, source base, and bit width.
• NOT is ambiguous without specifying the mask width; this review assumes NOT_x = (~x) AND (2^bit_width - 1).
• Shift operations are claimed but no shift amount or shift direction inputs are declared, and signed versus logical right shift is unspecified.
• Two's-complement behavior is ambiguous for values outside the selected width and for whether displayed values are unsigned bit patterns or signed integers.
• Supported source and output bases, digit syntax, leading-zero behavior, negative-input behavior, and fractional-input behavior are unspecified.

Units and conventions

• source_base is a dimensionless integer radix; these vectors use bases 10 and 16, with output bases 2, 8, 10, and 16.
• bit_width is an integer count of bits; NOT and shifts are masked to that width.
• number and bitwise operands are nonnegative integers representable in the selected width.
• shift is a nonnegative integer count in bits.
• Right shift is logical, and left shift discards bits beyond bit_width.
• Two's-complement signed value is interpreted as unsigned_value when its top bit is 0, otherwise unsigned_value - 2^bit_width.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "number": "173",
    "source_base": 10,
    "bit_width": 8,
    "operand": "90",
    "operation": "all",
    "shift": 2
  },
  "expected_outputs": {
    "binary": "10101101",
    "octal": "255",
    "decimal": 173,
    "hex": "AD",
    "twos_complement_signed": -83,
    "AND": {
      "binary": "10001000",
      "octal": "210",
      "decimal": 136,
      "hex": "88"
    },
    "OR": {
      "binary": "11111111",
      "octal": "377",
      "decimal": 255,
      "hex": "FF"
    },
    "XOR": {
      "binary": "01110111",
      "octal": "167",
      "decimal": 119,
      "hex": "77"
    },
    "NOT": {
      "binary": "01010010",
      "octal": "122",
      "decimal": 82,
      "hex": "52"
    },
    "left_shift_2": {
      "binary": "10110100",
      "octal": "264",
      "decimal": 180,
      "hex": "B4"
    },
    "logical_right_shift_2": {
      "binary": "00101011",
      "octal": "053",
      "decimal": 43,
      "hex": "2B"
    }
  },
  "working": "173 = 1×10^2 + 7×10 + 3 = 100 + 70 + 3. 173 = 128 + 32 + 8 + 4 + 1 = 10101101₂ = AD₁₆ = 255₈. 90 = 64 + 16 + 8 + 2 = 01011010₂. AND: 10101101 AND 01011010 = 10001000₂ = 136. OR: 10101101 OR 01011010 = 11111111₂ = 255. XOR: 10101101 XOR 01011010 = 01110111₂ = 119. NOT: 11111111₂ - 10101101₂ = 01010010₂ = 82. Signed two's complement: 173 - 256 = -83. Left shift: 173×2^2 = 692; 692 mod 256 = 180 = B4₁₆. Logical right shift: floor(173/2^2) = floor(43.25) = 43 = 2B₁₆."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The invalid base-2 digit input has no defined numeric value and must be rejected. The specification does not state the required validation behavior, and negative-input display conventions are also underspecified.

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