Subtraction using compliments:
Subtraction method mentioned earlier looks good when we do it on paper and pencil but to implement a subtraction method on a digital platform then subtraction using compliments is better and efficient.
r’s compliment:
If we are given numbers M & N with base r, then we can to have to find M – N then we can apply the following method:
If M and N both are positives then
 Take r’s compliment of subtrahend N
 Add the compliment to minuend M
 If we get a carry then discard it otherwise take r’s compliment of the result we get in step 2 and place –ve sign in front of this.
If M is negative and N is positive then i.e. – m – n where m & n are magnitudes of M&N
 Take r’s compliment of subtrahend N
 Add the compliment to minuend M
 If we get no carry then discard it otherwise if carry is 1 then, take r’s compliment of the result we get in step 2 and place –ve sign in front of this.
Eg. 76543_{10} – 66543_{10}
M=76543
N=66543
10’s compliment of N=33457
As both we ignore carry and answer we get is 0010 which is 2 (not 14) hence it is a wrong answer. It may seem very surprising as we have followed the proper procedure and yet not able to get the answer. Why???????????
Because we have to apply the 2^{nd} rule as M is negative and carry is 1 so we take 2’s compliment of the answer and final answer we get is – (2’s compliment of 0010_{2}) =  1110_{2} =  14_{10}
Eg. – 9_{10} – 10_{10}
Here we see – 10_{10} can be represented in 2’s compliment in 5 bits so we use 5 bits for both 9= 01001 10=01010
2’s compliment of 9 to represent 9 = 10111_{2}
2’s compliment of 10 to represent 10 = 10110_{2 }
As there is a carry so we’ll not ignore it as M is negative and we’ll calculate 2’s compliment of answer to get the actual answer
Answer=  (2’s compliment of 01101) =  10011 =  19_{10 }
And we find the correct answer
Eg. 26_{10} – 6_{10}
26 = 11010
6 = 00110
2’s compliment of 6 = 11010
We ignore the carry as M is positive and answer is 10100
Final answer = 10100 = 20 CORRECT
