Step 1

Compliment of Binary Numbers : In general, there are two sorts of Binary number complements: 1's complement and 2's complement. Simply invert the supplied number to get the 1's complement of a binary number. The 1s complement of the binary number 110010, for example, is 001101. To acquire the 2's complement of a binary number, add 1 to the least significant bit of the provided number (LSB). For example, the binary number 10010's 2's complement is (01101) + 1 = 01110.

2's Compliments - We locate one's complement first, then 2's complement. Starting with the LSB (least significant bit), we tour the one's complement in search of 0. We transform all 1's to 0's till we locate a 0. Finally, the detected 0 is flipped. The complement of "01000" is "11000," for example. (Note that one's complement of 01000 is first found as 10111.) We append an extra 1 to the string if there are all 1s (in one's complement). For example, "1000" is the 2nd complement of "000" (1st complement of "000" is "111").

Step 2

Signed bit Numbers - Positive numbers (including zero) are expressed as unsigned numbers in mathematics. That is, the +ve symbol is not used in front of them to indicate that they are positive values. When dealing with negative integers, however, we place a -ve sign in front of the number to indicate that it is less than a positive unsigned value, and the same is true for signed binary numbers. However, because digital systems function with binary numbers that are expressed in terms of "0's" and "1's," there is no provision in digital circuits to add a plus or even a minus sign to a number. These "1's" and "0's," referred to as bits (a contraction of Binary digit), fall into numerous range sizes of numbers that are referred to by common names, such as a byte or a word, when used together in microelectronics.

Subtraction using 2's Compliment -

1.Find the 2's complement of the subtrahend in the first step.
2.With the minuend, add the complement number.
3.If we receive the carry by adding both integers, we ignore it and the result is positive; otherwise, we take the result's 2's complement, which is negative.

Step 3 (i) M = 11010 N = 01101

We know that to find out two's compliment of any number first we take its 1's compliment in which we invert the all 0's to 1's and all 1's to 0's and then for 2's compliment we add 1 to the 1's compliment output

Find the 2's complement of the subtrahend in the first step- Step 1

(i) $M = 11010 N = 01101$

Here subtrahend is $N = 01101$

Taking it 2's compliment we get

= $01101$

= $10010$ (1's compliment)

Adding 1 in $10010$ to get 2's compliment of $N = 01101$

= $10010 + 1 10011$

Therefore 2's compliment of subtrahend is $1 0 0 1 1$

Step 4

With the minuend, add the complement number

On adding

$11010 + 10011 01101$

Here we got a carry of 1 and we know that If we receive the carry by adding both integers, we ignore it and the result is positive; otherwise, we take the result's 2's complement, which is negative.

So in this we can ignore the carry

Hence the result of subtraction is $0 1 1 0 1$

Now, checking it with direct subtraction method

$11010 - 01101 01101$

Hence answer is verified using direct subtraction method .

Step 5 (ii) M = 01010 N = 10000

We know that to find out two's compliment of any number first we take its 1's compliment in which we invert the all 0's to 1's and all 1's to 0's and then for 2's compliment we add 1 to the 1's compliment output

Find the 2's complement of the subtrahend in the first step- Step 1

(i) M = 01010 N = 10000

Here subtrahend is N=10000

Taking it 2's compliment we get

= 10000

= 01111 (1's compliment)

Adding 1 in $01111$ to get 2's compliment of N=10000

= $01111 + 1 10000$

Therefore 2's compliment of subtrahend is $1 0 0 0 0$

Step 6

With the minuend, add the complement number

On adding

$01010 + 10000 11010$

Here we got a carry of 1 and we know that If we receive the carry by adding both integers, we ignore it and the result is positive; otherwise, we take the result's 2's complement, which is negative.

So in this we can ignore the carry

Hence the result of subtraction is $1 1 0 1 0$

Now, checking it with direct subtraction method

$01010 - 10000 11010$

Hence answer is verified using direct subtraction method .

Step 7 (iii) M = 10010 N = 00001

We know that to find out two's compliment of any number first we take its 1's compliment in which we invert the all 0's to 1's and all 1's to 0's and then for 2's compliment we add 1 to the 1's compliment output

Find the 2's complement of the subtrahend in the first step- Step 1

(i) M = 10010 N = 00001

Here subtrahend is N=00001

Taking it 2's compliment we get

= 00001

= 11110 (1's compliment)

Adding 1 in $01111$ to get 2's compliment of N=10000

= $11110 + 1 11111$

Therefore 2's compliment of subtrahend is $1 1 1 1 1$

Step 8

With the minuend, add the complement number

On adding

$10010 + 11111 10001$

Here we got a carry of 1 and we know that If we receive the carry by adding both integers, we ignore it and the result is positive; otherwise, we take the result's 2's complement, which is negative.

So in this we can ignore the carry

Hence the result of subtraction is $1 0 0 0 1$

Now, checking it with direct subtraction method

$10010 - 00001 10001$

Hence answer is verified using direct subtraction method .

Using 2’s complement, perform M – N with the following signed 5-bit binary numbers. Also check the result by performing subtraction directly.(i) M = 11010 N = 01101(ii) M = 01010 N = 10000(iii) M = 10010 N = 00001

Public Answer

Using 2’s complement, perform M – N with the following signed 5-bit binary numbers. Also check the result by
performing subtraction directly.
(i) M = 11010 N = 01101
(ii) M = 01010 N = 10000
(iii) M = 10010 N = 00001