Diminished Radix Complement Representation:
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.
Decimal Number59 894 6578 2063 |
9’s Complement40 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;
Binary Number1011 1101 |
1’s Complement0100 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 -(2^{n-1} - 1) rather than -2^{n-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) 010100011’s complement 10101110 (ii) 10101000 1’s complement 01010111 |
Decimal Equivalent+81-127 + 46 = -81 -127 + 40 = -87 +87 |
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