Question

Convert the decimal numbers A and B to 5-bit binary numbers. Using two’s complement representation,

show (i) how to subtract the two 5-bit binary numbers (A−B);

(ii) how to translate the binary result back to decimal

Answer 1

To convert a given decimal no, to a 5 bit binary number we have to do divide the given no, by 2 until the remainder is 0

for example lets take 5

-----remainder -----------

2	5
2	2	1
2	1	0
	0	1

now read the remainder column in bottom up way

so you will get the order as 0 0 1 0 1 let it be A

similarly for any other number

so lets take another no, as 6

its binary number is 0 0 1 1 0 let it be B

now 5 bit binary subtraction for A-B

first of all u need to do is-

take the negative number and do 1's complement and then add 1 to the obtained result to make it as 2's complement

so ,now do 2's complement on B

step one ----- one's complement on    0 0 1 1 0

gives 1 1 0 0 1

now add 1 to it 1s

1 1 0 1 1 this is the 2s complement of B

now to do A-B  

we got the required format

now add the 2s complement of B and A to get the difference of A-B

carry bit 1 1 1 1 1

A------------ 0 0 1 0 1

B---------- +1 1 0 1 1

0 0 0 0 0 this the final binary number you would obtain

as the carry is 1 this indicates the result is negative and now you have to add that carry (1) to obtained result

then the result is now turns to 0 0 0 0 1 which is the required result .

2) so lets us check the obtained answer - 0 0 0 0 1

as we did 5-6 we get -1

now converting the obtained binary result to decimal number ---

okay lets now convert the result ----------- 1*2⁰+0*2¹+0*2²+0*2³+0*2⁴=1+0+0+0+0=1