Complement of a Number

Date: 7/10/96 at 10:51:3
From: Anonymous
Subject: Complement of a Number

What is the formula to find the complement of a number? 
What about the binary complement?

                               -Steve

Date: 7/11/96 at 18:15:51
From: Doctor Anthony
Subject: Re: Complement of a Number

To complement a number in base 10, you subtract it from a row of 9's. 
E.g. the complement of 5097 is 4912.  Likewise, in base 2, the 
complement of a number is obtained by subtraction from a row of 1's.  
All you have to do in fact is to interchange 0's and 1's. 
E.g. the complement of 10011101011 is
                       01100010100

In binary, a convenient way of subtraction is to add the complement.  
There is a slight complication when there is a carry 1 at the extreme 
left after the addition. In this case the carry 1 is moved to the 
extreme right and added. When making up the complement it is also 
necessary to make up the second number (with leading zeros if 
necessary) to the same number of digits as the first number before 
complementing.

Example. Find 101001101    Write this    101001101 
             -011100101                 +100011010
                                        -----------
                                        1001100111

Here we have a carry 1, so remove it and add to the extreme right hand 
column.  
                                         001100111
                                                 1
                                         ----------
                                           1101000 

-Doctor Anthony,  The Math Forum
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