C# BigInteger bitwise XOR returning extra digit [duplicate]

Question

Examples (asterisks next to odd behavior):

    [Fact]
    public void BigInteger_ToString_behavior_is_odd()
    {
        writeHex(new BigInteger(short.MaxValue)); // 7fff
        writeHex(new BigInteger(short.MaxValue) + 1); // 08000 **
        writeHex(new BigInteger(ushort.MaxValue)); // 0ffff **
        writeHex(new BigInteger(ushort.MaxValue) + 1); // 10000

        writeHex(new BigInteger(int.MaxValue)); // 7fffffff
        writeHex(new BigInteger(int.MaxValue) + 1); // 080000000 **
        writeHex(new BigInteger(uint.MaxValue)); // 0ffffffff **
        writeHex(new BigInteger(uint.MaxValue) + 1); // 100000000

        writeHex(new BigInteger(long.MaxValue)); // 7fffffffffffffff
        writeHex(new BigInteger(long.MaxValue) + 1); // 08000000000000000 **
        writeHex(new BigInteger(ulong.MaxValue)); // 0ffffffffffffffff **
        writeHex(new BigInteger(ulong.MaxValue) + 1); // 10000000000000000
    }

    private static void writeHex(BigInteger value)
    {
        Console.WriteLine(value.ToString("x"));
    }

• Is there a reason for this?
• How would I remove this extra zero? Can I just check if the string has a zero at the start and, if so, remove it? Any corner cases to think about?

Answer 1

Without a leading zero, the number may appear as though it is a negative number of the same number of bits in two's complement. Putting a leading zero ensures that the high bit isn't set, so it can't possibly be interpreted as a negative number.

Go ahead and remove the first character, if it's a zero, unless it's the only character in the string.