The "Sign Bit"

The algorithm that creates the repⁿ of the negative an integer works with both positive and negative integers. Start with N and complement it (make its negative): you get -N. Now complement -N and you get the original N.

0110 1101     →  1001 0010     add one →  1001 0011

1001 0011     reflect →  0110 1100     add one →  0110 1101

With N-bit two's comp repⁿ, the high order bit is "0" for positive integers and "1" for negative integers. This is a fortunate result. The high order bit is sometimes called the sign bit. But it is not really a sign (it does not play a separate role from the other bits). It takes part in the "binary addition algorithm" just as any bit.

 1001