The GATE Grind

GATE 2025 IN – Question 18

Digital Electronics · Number systems and combinational logic · 1 mark · Multiple choice

The 4-bit signed two’s-complement result of $(5)_{10}+(5)_{10}$ is

  1. $(-6)_{10}$
  2. $(-7)_{10}$
  3. $(-5)_{10}$
  4. $(-8)_{10}$

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Show answer and explanation

Correct answer: (A) $(-6)_{10}$

Explanation

Five is 0101.

Four-bit addition gives 0101+0101=1010.

Its signed two’s-complement interpretation is −8+2=**−6, A**.

The mathematical sum 10 lies outside the representable range −8 to 7, so signed overflow occurs.