Base Converter & Bitwise Toolkit

Inspectable records

Ledger state

The current ledger marks this instrument verified with errata that must be applied at binding time.

Area

Mathematics

Tranche

tranche-2

Evidence ID

t2-021

Ledger rows

1

No ledger note is attached.

Review findings

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.

Formula and scope findings

• 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.

Unit assumptions

• 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.

Boundary hardening

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.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "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."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

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

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