In the decimal number system the diminished radix complement is 9’s complement. This is obtained by subtracting each digit of the number from 9.

59

894

6578

2063

# 9’s Complement

40

105

3421

7936

The diminished radix complement of binary numbers is called 1’s complement. The 1’s complement of a binary number is formed by replacing each 1 in the number by a 0 and each 0 by 1.

For example, 1’s complements of some binary numbers are;

1011

1101

# 1’s Complement

0100

0010

In the case of signed magnitude representation of binary numbers, the MSB is the sign bit.

Positive number representations are same for both 1’s and 2’s complement. But representation of negative numbers differs by 1. A weight of -(2n-1 - 1) rather than -2n-1 is given to the MSB while computing the decimal equivalent of 1’s complement of a binary number.

A few examples of 8-bit binary numbers and their 1’s complement are given below;

# Binary Number

(i)                          01010001

1’s complement         10101110

(ii)                         10101000

1’s complement         01010111

# Decimal Equivalent

+81

-127 + 46 = -81

-127 + 40 = -87

+87

• Why Binary Numbers are Used
• Binary to Decimal Conversion
• Conversion of Numbers
• Hexa-decimal Number System
• Conversion of Binary Numbers to Octal or Hexa-decimal Numbers
• Octal and Hexa-Decimal Numbers
• Signed-magnitude Representation
• Arithmetic Operations of Binary Numbers