± Signed Number Representations

python

def twos_complement(val: int, bits: int = 8) -> str:
    """Convert signed integer to two's complement binary string."""
    mask = (1 << bits) - 1
    masked = val & mask if val < 0 else val
    return format(masked, f'0{bits}b')

def from_twos_complement(bin_str: str) -> int:
    """Convert two's complement binary string to signed integer."""
    bits = len(bin_str)
    val = int(bin_str, 2)
    if bin_str[0] == '1':
        val -= (1 << bits)
    return val

def detect_overflow(a_bin: str, b_bin: str, result_bin: str) -> bool:
    """Detect signed overflow in two's complement addition."""
    a_sign, b_sign, r_sign = a_bin[0], b_bin[0], result_bin[0]
    return a_sign == b_sign and a_sign != r_sign

# Examples
print(twos_complement(-5, 4))           # 1011
print(from_twos_complement("1011"))      # -5
print(detect_overflow("0111", "0010", "1001"))  # True (7+2=-7)