Exercise 3 solution

    def decode_signed(raw):
        value = int.from_bytes(raw, "big")
        bits = len(raw) * 8
        if value >= 1 << (bits - 1):
            value -= 1 << bits
        return value

    def encode_signed(value, size):
        if value < 0:
            value += 1 << (size * 8)
        return value.to_bytes(size, "big")

    for n in range(-128, 128):
        raw = encode_signed(n, 1)
        assert raw == n.to_bytes(1, "big", signed=True)
        assert decode_signed(raw) == n
    print("all 256 one-byte values agree")      # all 256 one-byte values agree
    print(decode_signed(b"\xff\xfe"), encode_signed(-2, 2).hex(" "))
                                                # -2 ff fe
    print(decode_signed(b"\x80\x00\x00\x00"), encode_signed(-1, 4).hex(" "))
                                                # -2147483648 ff ff ff ff

(Run as written; the output matched the comments.)

Explanation: in two's complement, a pattern whose top bit is set stands for
the unsigned value minus 2**bits. Decoding subtracts 2**bits when the value
is at or above 2**(bits - 1); encoding adds 2**bits to a negative number so
it fits in the unsigned range. The loop checks both functions against
Python's own signed=True handling for every possible one-byte value.