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