NIMCET 2014 — Computer PYQ

Solution

Concept:

• 1's complement: Inverting all the bits (changing $0$ to $1$ and $1$ to $0$).

• 2's complement: Adding $1$ to the Least Significant Bit (LSB) of the 1's complement.

  $$\text{2’s complement}=\text{1’s complement}+1\text{ (LSB)}$$

Step-by-Step Calculation:

1. Given Binary Number:

   $$0011010110011100$$

2. Find 1's Complement (Invert bits):

   $$1100101001100011$$

3. Find 2's Complement (Add 1 to LSB):

   \begin{array}{r@{\quad}c@{\quad}c@{\quad}c@{\quad}c} & 1100 & 1010 & 0110 & 0011 \\ + & & & & 1 \\ \hline & 1100 & 1010 & 0110 & 0100 \end{array}

Short Trick:

Start from the right (LSB) and keep all bits the same until you encounter the first '$1$'. Keep that '$1$' as it is, and then invert all the remaining bits to the left.

• Original: $0011010110011100$

• Result: $1100101001100100$

Conclusion:

The 2's complement of the given number is 1100 1010 0110 0100.