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X = 01110 and Y = 11001 are two 5-bit binary numbers represented in two’s complement format. The sum of X and Y represented in two’s complement format using 6 bits is
- a)110111
- b)001000
- c)000111
- d)101001
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
X = 01110 and Y = 11001 are two 5-bit binary numbers represented in tw...
's complement notation. To subtract Y from X using two's complement notation, we can follow the following steps:
1. Find the two's complement of Y:
- Invert all the bits in Y: 11001 becomes 00110.
- Add 1 to the inverted value: 00110 + 1 = 00111.
- The two's complement of Y is 00111.
2. Add X and the two's complement of Y:
- X = 01110
- Two's complement of Y = 00111
- X + two's complement of Y = 01110 + 00111 = 10101
3. Ignore the carry-out from the leftmost bit (if any), and the result is 0101.
Therefore, X - Y in two's complement notation is 0101.
1. Find the two's complement of Y:
- Invert all the bits in Y: 11001 becomes 00110.
- Add 1 to the inverted value: 00110 + 1 = 00111.
- The two's complement of Y is 00111.
2. Add X and the two's complement of Y:
- X = 01110
- Two's complement of Y = 00111
- X + two's complement of Y = 01110 + 00111 = 10101
3. Ignore the carry-out from the leftmost bit (if any), and the result is 0101.
Therefore, X - Y in two's complement notation is 0101.
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Community Answer
X = 01110 and Y = 11001 are two 5-bit binary numbers represented in tw...
To represent a given 5-bit number using 6- bits in a 2's complement representation, we simply copy the MSB bit as it is till we get the required 6 bits, i.e.
X = 01110 = 001110
Y = 11001 =111001
Ignoring the carry, we get the addition of the two in 2's complement number as:
∴ x + y = 000111
X = 01110 = 001110
Y = 11001 =111001
Ignoring the carry, we get the addition of the two in 2's complement number as:
∴ x + y = 000111
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X = 01110 and Y = 11001 are two 5-bit binary numbers represented in two’s complement format. The sum of X and Y represented in two’s complement format using 6 bits isa)110111b)001000c)000111d)101001Correct answer is option 'C'. Can you explain this answer?
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