IGDTUW 2026 — Computer PYQ

The correct option is (b) 0110.

Detailed Solution

To find the 2's complement of a binary number, we follow a simple two-step process:

Step 1: Find the 1's Complement

To get the 1's complement, invert all the bits of the given binary number (change $1$ to $0$ and $0$ to $1$).

$$\text{Original Binary Number}=1010$$

$$\text{1’s Complement}=0101$$

Step 2: Add 1 to the 1's Complement

To find the 2's complement, add $1$ (the Least Significant Bit, or LSB) to the 1's complement result.

\begin{array}{r@{\quad}l} 0101 & \text{(1's Complement)} \\ +\quad 0001 & \text{(Add 1)} \\ \hline 0110 & \text{(2's Complement)} \end{array}

$$\text{Binary Addition Break-down: }1+1=10\text{ (which is }0\text{ with a carry of }1\text{).}$$