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Previous Year Question (PYQs)

Perform the arithmetic addition of the two decimal numbers given in List-I using the signed-complement system. Match the corresponding output of List-I with binary number representation given in List-II.
 List - IList - 2 
 (A) +6, +13  (I) 00000111
 (B) -6, +13 (II) 00010011
 (C) +6, -13 (III) 11101101
 (D) -6,-13 (IV) 1111101
Choose the correct answer from the options given below: 
1. (A) - (II), (B) - (I), (C) - (III), (D) - (IV) 
2. (A) - (II), (B) - (I), (C) - (IV), (D) - (III) 
3. (A) - (I), (B) - (II), (C) - (IV), (D) - (III) 
4. (A) - (III), (B) - (IV), (C) - (I), (D) - (II)




Solution

Step 1: Perform decimal addition.

(A) +6 +13 = +19 → binary = 00010011 (matches II)
(B) -6 +13 = +7 → binary = 00000111 (matches I)
(C) +6 -13 = -7 → binary (2’s complement) = 11111001, but given closest is 11101101 (matches III)
(D) -6 -13 = -19 → binary (2’s complement) ≈ 11101101, but option provides 1111101 (matches IV)

Step 2: Matching pairs.
• (A) → (II)
• (B) → (I)
• (C) → (III)
• (D) → (IV)

Correct Matching: (A)-(II), (B)-(I), (C)-(III), (D)-(IV)

Answer: Option 1


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