Question

Match the Exclusive-OR (XOR) operations (i)–(iv) with the results (p)–(s), where $X$ is a Boolean input.

• A. (i)-(q), (ii)-(r), (iii)-(s), (iv)-(p)
• B. (i)-(q), (ii)-(r), (iii)-(p), (iv)-(s)
• C. (i)-(p), (ii)-(s), (iii)-(q), (iv)-(r)
• D. (i)-(q), (ii)-(p), (iii)-(s), (iv)-(r)

Hint:

Think of XOR as “toggle”: XOR with 0 leaves $X$ unchanged; XOR with 1 flips $X$; XOR with itself gives 0; XOR with its complement gives 1.

Answer 1

The Correct Option is D

Step 1: Recall XOR identities
- $X \oplus X = 0$ (same bits give 0). $\Rightarrow$ (i) $\to$ (q).
- $X \oplus \overline{X} = 1$ (different bits give 1). $\Rightarrow$ (ii) $\to$ (p).
- $X \oplus 0 = X$ (0 is the identity for XOR). $\Rightarrow$ (iii) $\to$ (s).
- $X \oplus 1 = \overline{X}$ (1 toggles the bit). $\Rightarrow$ (iv) $\to$ (r).
Final Answer: (i)-(q), (ii)-(p), (iii)-(s), (iv)-(r) $\Rightarrow$ Option (D).