FA-88856 / Digital logic simulation / Open access

XNOR output is not inverted · case 01

An XNOR gate returns the same value as XOR.

Verified by executionVariant 1 · 11 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The set of inverting gate types omits xnor, so its parity is returned uninverted.

VERIFIED REPAIR

Include every inverting gate type (nand, nor, xnor, not) in the output inversion set.

Unsuccessful approach: Adding xnor while dropping the plain inverter leaves NOT gates acting as buffers.

Case contract

Values are '0','1','x','z'. A 'z' on any gate input is read as 'x'. and/nand: any 0 -> 0, all 1 -> 1, else x; or/nor: any 1 -> 1, all 0 -> 0, else x; xor/xnor: any x -> x, else parity of ones; buf/not use the single input; nand/nor/xnor/not invert (x stays x). bufif1(data, enable): enable 0 -> 'z', enable x/z -> 'x', enable 1 -> data (z data becomes x).

Why this case matters

Gate-level logic simulators must propagate unknown and high-impedance values without inventing definite levels.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(*args):
    gate, ins = args
    def inv(v):
        return {'0': '1', '1': '0'}.get(v, 'x')
    ins = [('x' if v == 'z' else v) for v in ins]
    if gate == 'bufif1':
        d, e = ins
        return 'z' if e == '0' else ('x' if e == 'x' else d)
    if gate in ('and', 'nand'):
        r = '0' if '0' in ins else ('1' if all(v == '1' for v in ins) else 'x')
    elif gate in ('or', 'nor'):
        r = '1' if '1' in ins else ('0' if all(v == '0' for v in ins) else 'x')
    elif gate in ('xor', 'xnor'):
        r = 'x' if 'x' in ins else str(ins.count('1') % 2)
    else:
        r = ins[0]
    return inv(r) if gate in ('nand', 'nor', 'not') else r
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('and gate: controlling zero after unknowns', ['and', ['x', '0']], '0'), ('nand gate: all ones', ['nand', ['1', '1']], '0'), ('xor gate: floating input', ['xor', ['1', 'z']], 'x'), ('buffer of a floating net', ['buf', ['z']], 'x'), ('xor gate: two unknowns', ['xor', ['x', 'x']], 'x'), ('xnor gate: parity inversion', ['xnor', ['1', '0']], '0'), ('inverter control', ['not', ['1']], '0'), ('bufif1 unknown enable with low data', ['bufif1', ['0', 'x']], 'x'), ('bufif1 unknown enable with high data', ['bufif1', ['1', 'z']], 'x'), ('bufif1 disabled drives z', ['bufif1', ['1', '0']], 'z'), ('or gate: controlling one beside z', ['or', ['z', '1']], '1')], [('and gate: controlling zero after unknowns', ['and', ['x', 'x', '0']], '0'), ('nand gate: all ones', ['nand', ['1', '1', '1']], '0'), ('xor gate: floating input', ['xor', ['1', '1', 'z']], 'x'), ('buffer of a floating net', ['buf', ['z']], 'x'), ('xor gate: two unknowns', ['xor', ['x', 'x', '0']], 'x'), ('xnor gate: parity inversion', ['xnor', ['1', '1', '0']], '1'), ('inverter control', ['not', ['0']], '1'), ('bufif1 unknown enable with low data', ['bufif1', ['0', 'x']], 'x'), ('bufif1 unknown enable with high data', ['bufif1', ['1', 'z']], 'x'), ('bufif1 disabled drives z', ['bufif1', ['0', '0']], 'z'), ('or gate: controlling one beside z', ['or', ['z', 'z', '1']], '1')], [('and gate: controlling zero after unknowns', ['and', ['x', 'x', 'x', '0']], '0'), ('nand gate: all ones', ['nand', ['1', '1', '1', '1']], '0'), ('xor gate: floating input', ['xor', ['1', '1', '1', 'z']], 'x'), ('buffer of a floating net', ['buf', ['z']], 'x'), ('xor gate: two unknowns', ['xor', ['x', 'x', '0', '0']], 'x'), ('xnor gate: parity inversion', ['xnor', ['1', '1', '1', '0']], '0'), ('inverter control', ['not', ['1']], '0'), ('bufif1 unknown enable with low data', ['bufif1', ['0', 'x']], 'x'), ('bufif1 unknown enable with high data', ['bufif1', ['1', 'z']], 'x'), ('bufif1 disabled drives z', ['bufif1', ['1', '0']], 'z'), ('or gate: controlling one beside z', ['or', ['z', 'z', 'z', '1']], '1')], [('and gate: controlling zero after unknowns', ['and', ['x', 'x', 'x', 'x', '0']], '0'), ('nand gate: all ones', ['nand', ['1', '1', '1', '1', '1']], '0'), ('xor gate: floating input', ['xor', ['1', '1', '1', '1', 'z']], 'x'), ('buffer of a floating net', ['buf', ['z']], 'x'), ('xor gate: two unknowns', ['xor', ['x', 'x', '0', '0', '0']], 'x'), ('xnor gate: parity inversion', ['xnor', ['1', '1', '1', '1', '0']], '1'), ('inverter control', ['not', ['0']], '1'), ('bufif1 unknown enable with low data', ['bufif1', ['0', 'x']], 'x'), ('bufif1 unknown enable with high data', ['bufif1', ['1', 'z']], 'x'), ('bufif1 disabled drives z', ['bufif1', ['0', '0']], 'z'), ('or gate: controlling one beside z', ['or', ['z', 'z', 'z', 'z', '1']], '1')], [('and gate: controlling zero after unknowns', ['and', ['x', 'x', 'x', 'x', 'x', '0']], '0'), ('nand gate: all ones', ['nand', ['1', '1', '1', '1', '1', '1']], '0'), ('xor gate: floating input', ['xor', ['1', '1', '1', '1', '1', 'z']], 'x'), ('buffer of a floating net', ['buf', ['z']], 'x'), ('xor gate: two unknowns', ['xor', ['x', 'x', '0', '0', '0', '0']], 'x'), ('xnor gate: parity inversion', ['xnor', ['1', '1', '1', '1', '1', '0']], '0'), ('inverter control', ['not', ['1']], '0'), ('bufif1 unknown enable with low data', ['bufif1', ['0', 'x']], 'x'), ('bufif1 unknown enable with high data', ['bufif1', ['1', 'z']], 'x'), ('bufif1 disabled drives z', ['bufif1', ['1', '0']], 'z'), ('or gate: controlling one beside z', ['or', ['z', 'z', 'z', 'z', 'z', '1']], '1')]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
and gate: controlling zero after unknowns	`0`	`0`	Passed
nand gate: all ones	`0`	`0`	Passed
xor gate: floating input	`x`	`x`	Passed
buffer of a floating net	`x`	`x`	Passed
xor gate: two unknowns	`x`	`x`	Passed
xnor gate: parity inversion	`1`	`0`	Failed
inverter control	`0`	`0`	Passed
bufif1 unknown enable with low data	`x`	`x`	Passed
bufif1 unknown enable with high data	`x`	`x`	Passed
bufif1 disabled drives z	`z`	`z`	Passed
or gate: controlling one beside z	`1`	`1`	Passed

SHA-256 / 3ee162c216cd8354362f60d93ae6f40538897c74667058628f0617d6cd0e4138

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(*args):
    gate, ins = args
    def inv(v):
        return {'0': '1', '1': '0'}.get(v, 'x')
    ins = [('x' if v == 'z' else v) for v in ins]
    if gate == 'bufif1':
        d, e = ins
        return 'z' if e == '0' else ('x' if e == 'x' else d)
    if gate in ('and', 'nand'):
        r = '0' if '0' in ins else ('1' if all(v == '1' for v in ins) else 'x')
    elif gate in ('or', 'nor'):
        r = '1' if '1' in ins else ('0' if all(v == '0' for v in ins) else 'x')
    elif gate in ('xor', 'xnor'):
        r = 'x' if 'x' in ins else str(ins.count('1') % 2)
    else:
        r = ins[0]
    return inv(r) if gate in ('nand', 'nor', 'xnor') else r
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('and gate: controlling zero after unknowns', ['and', ['x', '0']], '0'), ('nand gate: all ones', ['nand', ['1', '1']], '0'), ('xor gate: floating input', ['xor', ['1', 'z']], 'x'), ('buffer of a floating net', ['buf', ['z']], 'x'), ('xor gate: two unknowns', ['xor', ['x', 'x']], 'x'), ('xnor gate: parity inversion', ['xnor', ['1', '0']], '0'), ('inverter control', ['not', ['1']], '0'), ('bufif1 unknown enable with low data', ['bufif1', ['0', 'x']], 'x'), ('bufif1 unknown enable with high data', ['bufif1', ['1', 'z']], 'x'), ('bufif1 disabled drives z', ['bufif1', ['1', '0']], 'z'), ('or gate: controlling one beside z', ['or', ['z', '1']], '1')], [('and gate: controlling zero after unknowns', ['and', ['x', 'x', '0']], '0'), ('nand gate: all ones', ['nand', ['1', '1', '1']], '0'), ('xor gate: floating input', ['xor', ['1', '1', 'z']], 'x'), ('buffer of a floating net', ['buf', ['z']], 'x'), ('xor gate: two unknowns', ['xor', ['x', 'x', '0']], 'x'), ('xnor gate: parity inversion', ['xnor', ['1', '1', '0']], '1'), ('inverter control', ['not', ['0']], '1'), ('bufif1 unknown enable with low data', ['bufif1', ['0', 'x']], 'x'), ('bufif1 unknown enable with high data', ['bufif1', ['1', 'z']], 'x'), ('bufif1 disabled drives z', ['bufif1', ['0', '0']], 'z'), ('or gate: controlling one beside z', ['or', ['z', 'z', '1']], '1')], [('and gate: controlling zero after unknowns', ['and', ['x', 'x', 'x', '0']], '0'), ('nand gate: all ones', ['nand', ['1', '1', '1', '1']], '0'), ('xor gate: floating input', ['xor', ['1', '1', '1', 'z']], 'x'), ('buffer of a floating net', ['buf', ['z']], 'x'), ('xor gate: two unknowns', ['xor', ['x', 'x', '0', '0']], 'x'), ('xnor gate: parity inversion', ['xnor', ['1', '1', '1', '0']], '0'), ('inverter control', ['not', ['1']], '0'), ('bufif1 unknown enable with low data', ['bufif1', ['0', 'x']], 'x'), ('bufif1 unknown enable with high data', ['bufif1', ['1', 'z']], 'x'), ('bufif1 disabled drives z', ['bufif1', ['1', '0']], 'z'), ('or gate: controlling one beside z', ['or', ['z', 'z', 'z', '1']], '1')], [('and gate: controlling zero after unknowns', ['and', ['x', 'x', 'x', 'x', '0']], '0'), ('nand gate: all ones', ['nand', ['1', '1', '1', '1', '1']], '0'), ('xor gate: floating input', ['xor', ['1', '1', '1', '1', 'z']], 'x'), ('buffer of a floating net', ['buf', ['z']], 'x'), ('xor gate: two unknowns', ['xor', ['x', 'x', '0', '0', '0']], 'x'), ('xnor gate: parity inversion', ['xnor', ['1', '1', '1', '1', '0']], '1'), ('inverter control', ['not', ['0']], '1'), ('bufif1 unknown enable with low data', ['bufif1', ['0', 'x']], 'x'), ('bufif1 unknown enable with high data', ['bufif1', ['1', 'z']], 'x'), ('bufif1 disabled drives z', ['bufif1', ['0', '0']], 'z'), ('or gate: controlling one beside z', ['or', ['z', 'z', 'z', 'z', '1']], '1')], [('and gate: controlling zero after unknowns', ['and', ['x', 'x', 'x', 'x', 'x', '0']], '0'), ('nand gate: all ones', ['nand', ['1', '1', '1', '1', '1', '1']], '0'), ('xor gate: floating input', ['xor', ['1', '1', '1', '1', '1', 'z']], 'x'), ('buffer of a floating net', ['buf', ['z']], 'x'), ('xor gate: two unknowns', ['xor', ['x', 'x', '0', '0', '0', '0']], 'x'), ('xnor gate: parity inversion', ['xnor', ['1', '1', '1', '1', '1', '0']], '0'), ('inverter control', ['not', ['1']], '0'), ('bufif1 unknown enable with low data', ['bufif1', ['0', 'x']], 'x'), ('bufif1 unknown enable with high data', ['bufif1', ['1', 'z']], 'x'), ('bufif1 disabled drives z', ['bufif1', ['1', '0']], 'z'), ('or gate: controlling one beside z', ['or', ['z', 'z', 'z', 'z', 'z', '1']], '1')]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
and gate: controlling zero after unknowns	`0`	`0`	Passed
nand gate: all ones	`0`	`0`	Passed
xor gate: floating input	`x`	`x`	Passed
buffer of a floating net	`x`	`x`	Passed
xor gate: two unknowns	`x`	`x`	Passed
xnor gate: parity inversion	`0`	`0`	Passed
inverter control	`1`	`0`	Failed
bufif1 unknown enable with low data	`x`	`x`	Passed
bufif1 unknown enable with high data	`x`	`x`	Passed
bufif1 disabled drives z	`z`	`z`	Passed
or gate: controlling one beside z	`1`	`1`	Passed

SHA-256 / d6a1f2d3563416122f4bf75010eea4f19947e94cb974bfb1f302037efb804374

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(*args):
    gate, ins = args
    def inv(v):
        return {'0': '1', '1': '0'}.get(v, 'x')
    ins = [('x' if v == 'z' else v) for v in ins]
    if gate == 'bufif1':
        d, e = ins
        return 'z' if e == '0' else ('x' if e == 'x' else d)
    if gate in ('and', 'nand'):
        r = '0' if '0' in ins else ('1' if all(v == '1' for v in ins) else 'x')
    elif gate in ('or', 'nor'):
        r = '1' if '1' in ins else ('0' if all(v == '0' for v in ins) else 'x')
    elif gate in ('xor', 'xnor'):
        r = 'x' if 'x' in ins else str(ins.count('1') % 2)
    else:
        r = ins[0]
    return inv(r) if gate in ('nand', 'nor', 'xnor', 'not') else r
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('and gate: controlling zero after unknowns', ['and', ['x', '0']], '0'), ('nand gate: all ones', ['nand', ['1', '1']], '0'), ('xor gate: floating input', ['xor', ['1', 'z']], 'x'), ('buffer of a floating net', ['buf', ['z']], 'x'), ('xor gate: two unknowns', ['xor', ['x', 'x']], 'x'), ('xnor gate: parity inversion', ['xnor', ['1', '0']], '0'), ('inverter control', ['not', ['1']], '0'), ('bufif1 unknown enable with low data', ['bufif1', ['0', 'x']], 'x'), ('bufif1 unknown enable with high data', ['bufif1', ['1', 'z']], 'x'), ('bufif1 disabled drives z', ['bufif1', ['1', '0']], 'z'), ('or gate: controlling one beside z', ['or', ['z', '1']], '1')], [('and gate: controlling zero after unknowns', ['and', ['x', 'x', '0']], '0'), ('nand gate: all ones', ['nand', ['1', '1', '1']], '0'), ('xor gate: floating input', ['xor', ['1', '1', 'z']], 'x'), ('buffer of a floating net', ['buf', ['z']], 'x'), ('xor gate: two unknowns', ['xor', ['x', 'x', '0']], 'x'), ('xnor gate: parity inversion', ['xnor', ['1', '1', '0']], '1'), ('inverter control', ['not', ['0']], '1'), ('bufif1 unknown enable with low data', ['bufif1', ['0', 'x']], 'x'), ('bufif1 unknown enable with high data', ['bufif1', ['1', 'z']], 'x'), ('bufif1 disabled drives z', ['bufif1', ['0', '0']], 'z'), ('or gate: controlling one beside z', ['or', ['z', 'z', '1']], '1')], [('and gate: controlling zero after unknowns', ['and', ['x', 'x', 'x', '0']], '0'), ('nand gate: all ones', ['nand', ['1', '1', '1', '1']], '0'), ('xor gate: floating input', ['xor', ['1', '1', '1', 'z']], 'x'), ('buffer of a floating net', ['buf', ['z']], 'x'), ('xor gate: two unknowns', ['xor', ['x', 'x', '0', '0']], 'x'), ('xnor gate: parity inversion', ['xnor', ['1', '1', '1', '0']], '0'), ('inverter control', ['not', ['1']], '0'), ('bufif1 unknown enable with low data', ['bufif1', ['0', 'x']], 'x'), ('bufif1 unknown enable with high data', ['bufif1', ['1', 'z']], 'x'), ('bufif1 disabled drives z', ['bufif1', ['1', '0']], 'z'), ('or gate: controlling one beside z', ['or', ['z', 'z', 'z', '1']], '1')], [('and gate: controlling zero after unknowns', ['and', ['x', 'x', 'x', 'x', '0']], '0'), ('nand gate: all ones', ['nand', ['1', '1', '1', '1', '1']], '0'), ('xor gate: floating input', ['xor', ['1', '1', '1', '1', 'z']], 'x'), ('buffer of a floating net', ['buf', ['z']], 'x'), ('xor gate: two unknowns', ['xor', ['x', 'x', '0', '0', '0']], 'x'), ('xnor gate: parity inversion', ['xnor', ['1', '1', '1', '1', '0']], '1'), ('inverter control', ['not', ['0']], '1'), ('bufif1 unknown enable with low data', ['bufif1', ['0', 'x']], 'x'), ('bufif1 unknown enable with high data', ['bufif1', ['1', 'z']], 'x'), ('bufif1 disabled drives z', ['bufif1', ['0', '0']], 'z'), ('or gate: controlling one beside z', ['or', ['z', 'z', 'z', 'z', '1']], '1')], [('and gate: controlling zero after unknowns', ['and', ['x', 'x', 'x', 'x', 'x', '0']], '0'), ('nand gate: all ones', ['nand', ['1', '1', '1', '1', '1', '1']], '0'), ('xor gate: floating input', ['xor', ['1', '1', '1', '1', '1', 'z']], 'x'), ('buffer of a floating net', ['buf', ['z']], 'x'), ('xor gate: two unknowns', ['xor', ['x', 'x', '0', '0', '0', '0']], 'x'), ('xnor gate: parity inversion', ['xnor', ['1', '1', '1', '1', '1', '0']], '0'), ('inverter control', ['not', ['1']], '0'), ('bufif1 unknown enable with low data', ['bufif1', ['0', 'x']], 'x'), ('bufif1 unknown enable with high data', ['bufif1', ['1', 'z']], 'x'), ('bufif1 disabled drives z', ['bufif1', ['1', '0']], 'z'), ('or gate: controlling one beside z', ['or', ['z', 'z', 'z', 'z', 'z', '1']], '1')]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
and gate: controlling zero after unknowns	`0`	`0`	Passed
nand gate: all ones	`0`	`0`	Passed
xor gate: floating input	`x`	`x`	Passed
buffer of a floating net	`x`	`x`	Passed
xor gate: two unknowns	`x`	`x`	Passed
xnor gate: parity inversion	`0`	`0`	Passed
inverter control	`0`	`0`	Passed
bufif1 unknown enable with low data	`x`	`x`	Passed
bufif1 unknown enable with high data	`x`	`x`	Passed
bufif1 disabled drives z	`z`	`z`	Passed
or gate: controlling one beside z	`1`	`1`	Passed

SHA-256 / bf15fc3a903151bbaa24735361c943b11c86bac06ef93c0a5eee525770f8f941

Verification & scope

A deterministic bounded teaching model of one simulator rule set; the contract is stipulated and is not a claim of conformance to any HDL standard or commercial simulator. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:51:12.029475+00:00.

Case digest / 464b374f675a95e3dc1c72f8bd315b68b257f6f095863eb951c838c5319ba11f