Programming

Calculating 2's Compliment

A Positive Number

is represented as a simple unsigned binary.

A Negative Number

is represented as the binary number that when added to a positive number of the same magnitude equals zero.

To form a negative number:

• first compliment each bit of the positive number (i.e., change all of the 1's to 0's, and vice versa; this is called the "1's compliment"),
• then add 1.

For example,

Most Significant Bit (MSB) indicates the sign of the integer.

 

If MSB = 0, then the number is greater than or equal to 0.

 

If MSB = 1, then the number is less than 0.

2's Compliment Arithmetic

Notes

1. 0 + 0 = 0
2. 0 + 1 = 1
3. 1 + 0 = 1
4. 1 + 1 = 0, and carry 1 to the next more significant bit

1. 0 - 0 = 0
2. 0 - 1 = 1, and borrow 1 from the next more significant bit
3. 1 - 0 = 1
4. 1 - 1 = 0

1. 0 x 0 = 0
2. 0 x 1 = 0
3. 1 x 0 = 0
4. 1 x 1 = 1, and no carry or borrow bits

This page is for INFORMATIONAL PURPOSES ONLY.