X = 00110 and Y = 10011 are two binary numbers represented in 2s complement format. The sum of X and Y represented in 2s complement format using 5 bits is _____a)11001b)01001c)10100d)10010Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Explanation:

1. Convert X and Y to decimal:
X = 00110 -> -2 (in decimal)
Y = 10011 -> -13 (in decimal)

2. Add X and Y:
-2 + (-13) = -15

3. Convert the result back to binary:
-15 in binary is 10001

4. Represent 10001 in 5 bits 2s complement:
Since the result is negative, we need to represent it in 2s complement form.
10001 in 5 bits 2s complement is 10001

Therefore, the sum of X and Y represented in 2s complement format using 5 bits is 10001, which is equivalent to -15 in decimal.

Hence, the correct answer is option 'A' - 11001.

Answer

X = 00110
since, the MSB = 0
∴ it is a positive number.
Decimal equivalent: 0 + 1 × 22 + 1 × 21 + 0 × 20 = + 6
Y = 10011
since, the MSB = 1
∴ it is a negative number,
We need to take the 2's complement of Y, that is.
1's complement (Y) + 1
01100 + 1
⇒ 01101
Decimal equivalent → 0 + 1 × 23 + 1 × 22 + 0 + 1 × 20 → -13
The sum of X and Y is
+6 - 13 = - 7
The 2's complement of - 7
→ 1's complement of 7 + 1
→ 1's complement of 00111 + 1
→ 11000 + 1 → 11001

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