Binary subtraction

Binary subtraction

Before explaining subtraction lets see how negative numbers are represented in binary. To denote the sign of a binary number a extra bit is used in the left end of the number. By convention zero is used to represent + sign and a one is used to represent -sign.

+5 = 0,101

-7 = 1,111

Subtraction is the process of adding a negative number to a positive number. If a number having a positive sign is added to a number with a number y having a negative sign ,it is equivalent to subtracting y from x.

Consider the example below

101-011

Borrow	1	0
Minuend	1	0	1
Subtrahend	0	1	1
Difference	0	1	0

Borrow	0
Minuend	0
Subtrahend	0
Difference	0

Borrow	1
Minuend	0
Subtrahend	1
Difference	1

From the above examples we can construct a half subtracter table and full subtracter table.

Half subtracter

a	b                                       Difference             Borrow
0	0	0	0
0	1	1	1
1	0	1	0
1	1	0	0

Full subtracter

A(Minuend)	B(Subtrahend)	Borrow	Difference	Borrow to next position
0	0	0	0	0
0	0	1	1	1
0	1	0	1	1
0	1	1	0	1
1	0	0	1	0
1	0	1	0	0
1	1	0	0	0
1	1	1	1	1