Two values for zero:

0000 0000 0000 0000   &   1000 0000 0000 0000

are both zero. The most significant bit is the sign: 0 for positive and 1 for negative.

(A - B) is not the same as (A + (-B), and it should be!

52	=	00110100		52	=	00110100
- 31	=	- 00011111		- 31	=	- 10011111
----		----------		----		----------
21	=	00010101		21	!=	11010011

Two values for zero:

0000 0000 0000 0000   &   1111 1111 1111 1111

are both zero. The most significant bit is the sign: 0 for positive and 1 for negative. Here as in Signed Magnitude, the computer processor must have extra circuitry to check for this after every operation.

In this case (A - B) is the same as (A + (-B):

52	=	00110100		52	=	00110100
- 31	=	- 00011111		- 31	=	- 11100000
----		----------				----------
21	=	00010101				111010011
						+ 1
				----		----------
				21	=	00010101

The processor must add 1 to the binary number if the operation results in an overflow.

The designer of the processor can use addition circuitry for subtraction by making the second operand negative.

Form the One's Complement and add 1.

- 31	becomes	11100000
		+ 1
		----------
		11100001
-(-31)	becomes	00011110
		+ 1
		----------
		00011111	As it should be