Before doing anything, we need to decide if the two’s complement is a positive or negative number.

Firstly you need to look at the most significant bit (the leftmost bit); if it is a 0 then it is positive and simply convert the number to decimal. For example:

128	64	32	16	8	4	2	1
0	0	1	0	0	1	0	1

Because the leftmost bit is a 0 then we know the number is positive so we simply add

32 + 4 + 1 = +37.

Negative two’s complement number

If the most significant bit (the leftmost bit); is a 1 then we have to convert the number to a positive number then work out the denary equivalent. 

You do this in exactly the same way you converted a positive number to negative i.e.

1. invert all the bits (so a 1 becomes a 0 and a 0 becomes a 1)
2. then add 1
3. convert to denary.

Example

Convert the two’s complement binary number 11111011 to denary.

128	64	32	16	8	4	2	1
1	1	1	1	1	0	1	1

Because the most significant bit is a 1, we know it is a negative number therefore we need to convert it to a positive number first.

Change all the 1’s to 0 and 0’s to 1.

0 0 0 0 0 1 0 0

Add 1.

0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 1 +
0 0 0 0 0 1 0 1

So 00000101 as Two’s Complement = -5