Radix Complement Representation:
In the decimal number system, the radix complement is the 10’s complement. In radix complement representation system, the complement of an n-digit number is obtained by subtracting the number from 10_{n}.
Let us consider some examples of 3-digit numbers and their radix complement in decimal system.
Decimal Number948 607 155 735 |
Radix Complement52 393 845 265 |
Therefore, the 10’s complement of the number N is obtained by subtracting each digit of the number from 9 and then adding 1 to the LSD of the number so formed.
For instance, the 10’s complement of 172 is (827 + 1) or 828 and that of 405 is (594 + 1) or 595.
For the binary number system the radix complement is the two’s complement. The 2’s complement of a binary number is obtained by subtracting each bit of the number from the radix diminished by 1 i.e. from (2 - 1) or 1 and adding an 1 to the LSB. The application of this rule is very simple. We have to just change 1 to 0 and 0 to 1 in every bit and then add 1 to the LSB of the number so formed. For example, the 2’s complement of the binary number 11011 is (00100 + 1) or 00101 and that of 10110 is (01001 + 1) or 01010.
If the number be in signed magnitude representation, it is positive if the MSB is 0 and negative if the MSB is 1. The decimal equivalent of a 2’s complement binary number, in the case of signed-magnitude representation, is computed in the same way as for an unsigned number except that the weight of the MSB is -2^{n-1} instead of +2^{n-1} for an n-bit binary number.
Let us observe some examples of 8-bit binary numbers and their 2’s complement are shown below:
Binary NumberSign bit 01101101Complement: 10010010 + 1 10010011 |
Decimal equivalent+ 109- 128 + 19 = -109 |
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