The GATE Grind

GATE 2023 IN – Question 17

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

Match XOR operations i–iv to results p–s, where $X$ is a Boolean input.

Operations: i. $X\oplus X$; ii. $X\oplus\bar X$; iii. $X\oplus0$; iv. $X\oplus1$.

Results: p. $1$; q. $0$; r. $\bar X$; s. $X$.

  1. (i) - (q), (ii) - (r), (iii) - (s), (iv) - (p)
  2. (i) - (q), (ii) - (r), (iii) - (p), (iv) - (s)
  3. (i) - (p), (ii) - (s), (iii) - (q), (iv) - (r)
  4. (i) - (q), (ii) - (p), (iii) - (s), (iv) - (r)

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Show answer and explanation

Correct answer: (D) (i) - (q), (ii) - (p), (iii) - (s), (iv) - (r)

Explanation

XOR identities give $X\oplus X=0$, $X\oplus\bar X=1$, $X\oplus0=X$, and $X\oplus1=\bar X$.

Thus i–q, ii–p, iii–s, iv–r, **D**.