IGDTUW 2025 — Computer PYQ

The correct answer is (a) Only one arithmetic operation is required.

Conceptual Breakdown

The 2's complement system is the standard method for representing signed integers in modern digital computers. Its primary advantage lies in simplifying hardware design for arithmetic units.

• Unified Arithmetic: In a sign-magnitude system, addition and subtraction require different hardware logic because the sign bit must be handled separately.

• Simplified Hardware: In the 2's complement system, subtraction is performed as addition. To subtract a number $B$ from $A$ (i.e., $A-B$), the computer simply calculates $A+(-B)$, where $-B$ is the 2's complement representation of $B$.

Mathematical Representation

In 2's complement, the subtraction operation $A-B$ is transformed into:

$$A-B=A+(\text{2’s complement of }B)$$

By utilizing this property, a CPU's Arithmetic Logic Unit (ALU) does not require a separate subtraction circuit. It can use the same adder circuit for both addition and subtraction.

• Let $A=5$ (binary 0101)

• Let $B=3$ (binary 0011)

• To calculate $A-B$:

  1. Find 2's complement of $3$ (0011):

     • Invert bits: 1100

     • Add $1$: 1101 (this represents $-3$ in 4-bit 2's complement)

  2. Add $A$ and $(-B)$:

     • 0101 + 1101 = 10010

  3. Ignore the carry bit (overflow): Result is 0010, which equals $2$.