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A signed integer has been stored in a byte using 2’s complement format. We wish to store the same integer in 16-bit word. We should copy the original byte to the less significant byte of the word and fill the more significant byte with
- a)0
- b)1
- c)equal to the MSB of the original byte
- d)complement of the MSB of the original byte.
Correct answer is option 'C'. Can you explain this answer?
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A signed integer has been stored in a byte using 2’s complement ...
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A signed integer has been stored in a byte using 2’s complement ...
Explanation:
Storing a signed integer using 2s complement format means that the most significant bit (MSB) of the byte represents the sign of the number. If the MSB is 0, the number is positive, and if it is 1, the number is negative.
When we wish to store the same integer in a 16-bit word, we need to copy the original byte to the less significant byte of the word. This means that the original byte will occupy the first 8 bits of the 16-bit word.
The remaining 8 bits of the word need to be filled in such a way that the sign of the number is preserved. This is where the options (a) to (d) come in.
Option (a) is incorrect because filling the more significant byte with 0 will change the sign of the number. For example, if the original byte is 10000001, which represents a negative number, filling the more significant byte with 0 will change it to 00000001, which represents a positive number.
Option (b) is also incorrect because filling the more significant byte with 1 will change the value of the number. For example, if the original byte is 00000001, which represents a positive number, filling the more significant byte with 1 will change it to 11111111, which represents a negative number.
Option (c) is the correct answer because filling the more significant byte with the MSB of the original byte will preserve the sign of the number. For example, if the original byte is 10000001, which represents a negative number, filling the more significant byte with 1 will result in 11111111, which is the 2s complement representation of a negative number.
Option (d) is incorrect because taking the complement of the MSB of the original byte will change the sign of the number. For example, if the original byte is 10000001, which represents a negative number, taking the complement of the MSB (which is 1) will result in 0, which represents a positive number.
In summary, when storing a signed integer in a 16-bit word, we should copy the original byte to the less significant byte of the word and fill the more significant byte with the MSB of the original byte to preserve the sign of the number.
Storing a signed integer using 2s complement format means that the most significant bit (MSB) of the byte represents the sign of the number. If the MSB is 0, the number is positive, and if it is 1, the number is negative.
When we wish to store the same integer in a 16-bit word, we need to copy the original byte to the less significant byte of the word. This means that the original byte will occupy the first 8 bits of the 16-bit word.
The remaining 8 bits of the word need to be filled in such a way that the sign of the number is preserved. This is where the options (a) to (d) come in.
Option (a) is incorrect because filling the more significant byte with 0 will change the sign of the number. For example, if the original byte is 10000001, which represents a negative number, filling the more significant byte with 0 will change it to 00000001, which represents a positive number.
Option (b) is also incorrect because filling the more significant byte with 1 will change the value of the number. For example, if the original byte is 00000001, which represents a positive number, filling the more significant byte with 1 will change it to 11111111, which represents a negative number.
Option (c) is the correct answer because filling the more significant byte with the MSB of the original byte will preserve the sign of the number. For example, if the original byte is 10000001, which represents a negative number, filling the more significant byte with 1 will result in 11111111, which is the 2s complement representation of a negative number.
Option (d) is incorrect because taking the complement of the MSB of the original byte will change the sign of the number. For example, if the original byte is 10000001, which represents a negative number, taking the complement of the MSB (which is 1) will result in 0, which represents a positive number.
In summary, when storing a signed integer in a 16-bit word, we should copy the original byte to the less significant byte of the word and fill the more significant byte with the MSB of the original byte to preserve the sign of the number.
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A signed integer has been stored in a byte using 2’s complement ...
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