2’s Complement Number

2’s Complement Number

Definition:

Property

Two's complement representation allows the use of binary arithmetic operations on signed integers, yielding the correct 2's complement results.

Positive Numbers

Positive 2's complement numbers are represented as the simple binary.

Negative Numbers

Negative 2's complement numbers are represented as the binary number that when added to a positive number of the same magnitude equals zero.

How to Calculate 2's Complement?

For example: -20₁₀

Separate the sign and magnitude number of -1. The sign will be 1 if the number is negative and will be 0 if the number is positive.

Sign	Magnitude	Note
0	0010100	Now is 20
	1101011	Each 0 is changed to a 1 and each 1 is changed to a 0
	1101100	Add + 1
1	1101100	Now is -20

2's Complement Addition

1)    30₁₀ – 20₁₀

30₁₀ = 00011110₂

-20₁₀ = 11101100₂

Therefore, 00011110₂ + 11101100_{2 =} 00001010₂ = 10₁₀