Question

What is the advantage of 2’s complement over 1s’ complement in negative number representation in binary number system? How does it affect the range of values stored in a certain bit representation of number in binary system?

Answer 1

The primary advantage of two’s complement over ones’ complement is that two’s complement only has one value for zero. Ones’ complement has a "positive" zero and a "negative" zero.

Next, to add numbers using one’s complement you have to first do binary addition, then add in an end-around carry value.

Two’s complement has only one value for zero, and doesn’t require carry values.

You also asked how the range of values stored are affected. Consider an eight-bit integer value, the following are your minimum and maximum values:

Notation	Min	Max
Unsigned:	0	255
One’s Comp:	-127	+127
Two’s Comp:	-128	+127

References:

• http://en.wikipedia.org/wiki/Signed_number_representations
• http://en.wikipedia.org/wiki/Ones%27_complement
• http://en.wikipedia.org/wiki/Two%27s_complement