def encode_sign_magnitude(value: int, sign_bit_index: int):
    """
    https://en.wikipedia.org/wiki/Signed_number_representations#Sign%E2%80%93magnitude
    """
    max_magnitude = (1 << sign_bit_index) - 1
    magnitude = abs(value)
    if magnitude > max_magnitude:
        raise ValueError(f"Magnitude {magnitude} exceeds {max_magnitude} (max for {sign_bit_index=})")

    direction_bit = 1 if value < 0 else 0
    return (direction_bit << sign_bit_index) | magnitude


def decode_sign_magnitude(encoded_value: int, sign_bit_index: int):
    """
    https://en.wikipedia.org/wiki/Signed_number_representations#Sign%E2%80%93magnitude
    """
    direction_bit = (encoded_value >> sign_bit_index) & 1
    magnitude_mask = (1 << sign_bit_index) - 1
    magnitude = encoded_value & magnitude_mask
    return -magnitude if direction_bit else magnitude


def encode_twos_complement(value: int, n_bytes: int):
    """
    https://en.wikipedia.org/wiki/Signed_number_representations#Two%27s_complement
    """

    bit_width = n_bytes * 8
    min_val = -(1 << (bit_width - 1))
    max_val = (1 << (bit_width - 1)) - 1

    if not (min_val <= value <= max_val):
        raise ValueError(
            f"Value {value} out of range for {n_bytes}-byte two's complement: [{min_val}, {max_val}]"
        )

    if value >= 0:
        return value

    return (1 << bit_width) + value


def decode_twos_complement(value: int, n_bytes: int) -> int:
    """
    https://en.wikipedia.org/wiki/Signed_number_representations#Two%27s_complement
    """
    bits = n_bytes * 8
    sign_bit = 1 << (bits - 1)
    if value & sign_bit:
        value -= 1 << bits
    return value