Question

100110-1101 binary subtraction ​

Answer 1

Ans:-100110-1101 binary subtraction

Answer 2

Subtracting (1101)₂ from (100110)₂ we get (11001)₂

Correct question : Subtract (1101)₂ from (100110)₂

Given :

The binary numbers (1101)₂ and (100110)₂

To find :

Subtract (1101)₂ from (100110)₂

Process :

Subtraction by 1’s complement method :

1. Write down the given binary numbers. Mention minuend and subtrahend

2. Find 1’s complement of the subtrahend

3. Add the number obtained with the minuend

4. If result obtained after addition has a carry over then it is dropped and add 1 with the last bit

5. If result obtained after addition has no carry over, then find 1’s complement of the result obtained after addition. The number obtained is the required number but the number will be negative.

Solution :

Step 1 of 4 :

Write down the given binary numbers. Mention minuend and subtrahend

Here the given binary numbers are (1101)₂ and (100110)₂

Subtrahend = (1101)₂ = (001101)₂

Minuend = (100110)₂

Step 2 of 4 :

Find 1’s complement of the subtrahend

1’s complement of the subtrahend

= 1’s complement of (001101)₂

= (110010)₂

Step 3 of 4 :

Add the number obtained with the minuend

$\qquad\begin{gathered}\boxed{\begin{array}{c } \sf \: \: \: \: \: 100110 \\ \sf + \: \: 110010 \\ \frac{\qquad \qquad}{} & \\ \sf \: \: \: \: \boxed{1}011000\end{array}} \\ \end{gathered}$

Step 4 of 4 :

Find the required number

The result obtained after addition has a carry over [ Carry over is marked in box ]

So it is dropped and we add 1 with the last bit

$\qquad\begin{gathered}\boxed{\begin{array}{c } \sf \: \: \: \: \: 011000 \\ \sf + \: \: \: \: \: \: \: \: \: \: \: \: \: 1 \\ \frac{\qquad \qquad}{} & \\ \sf \: \: \: \: \: \: 011001\end{array}} \\ \end{gathered}$

Hence the required number = (11001)₂

∴ Subtracting (1101)₂ from (100110)₂ we get (11001)₂

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