Number System and Representation                                                                                                        Print this page
<< Previous |  First |  Last |  Next >>       

Radix Complement :

The r’s complement of an n-digit number in base r is defined as for N != 0   and    0 for N = 0.
r’s complement is obtained by adding 1 to the ( r - 1 )’s complement,  since
          e.g.,  10's  complement of   5642  is  9's  complement  of  5642 + 1,   i.e.,  4357 + 1  = 4358
          e.g.,    2's  complement of   1010  is  1's  complement  of  1010 + 1,   i.e.,  0101 + 1  = 0110.

Representation of Signed integer in 1's complement form:

Consider the eight bit number 01011100, 1's complements of this number is 10100011. If we perform the following addition:

If we add 1 to the number, the result is 100000000.

 

0  1  0  1  1  1  0  0

1  0  1  0  0  0  1  1
----------------------------

1  1  1  1  1  1  1  1

Since we are considering an eight bit number, so the 9th bit (MSB) of the result can not be stored. Therefore, the final result is 00000000.

Since the addition of two number is 0, so one can be treated as the negative of the other number. So, 1's complement can be used to represent negative number.

<< Previous |  First |  Last |  Next >>