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Let X be the number of distinct 16-bit integers in 2`s complement representation. Let Y be the number of distinct -bit integers in sign magnitude representation Then X Y is______.
Correct answer is '1'. Can you explain this answer?
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Let X be the number of distinct 16-bit integers in 2`s complement repr...
For N bits, Distinct values represented in 2's complement is -2n-1 to 2n-1 -1
Distinct values represented in Signed Magnitude is -(2n-1 -1) to 2n-1 -1
Difference is 1.
Distinct values represented in Signed Magnitude is -(2n-1 -1) to 2n-1 -1
Difference is 1.
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Let X be the number of distinct 16-bit integers in 2`s complement repr...
Number of distinct 16-bit integers in 2's complement representation (X)
To find the number of distinct 16-bit integers in 2's complement representation, we need to consider the range of values that can be represented using 16 bits in 2's complement.
Range of 2's complement representation
In 2's complement representation, the leftmost bit (MSB) is reserved for sign, and the remaining bits represent the magnitude of the number. The MSB is 0 for positive numbers and 1 for negative numbers.
For a 16-bit representation, the MSB can be either 0 or 1, giving us two possibilities. The remaining 15 bits can represent values from 0 to 2^15-1 (since the MSB is reserved for sign). Therefore, the total number of distinct 16-bit integers in 2's complement representation is:
X = 2 * 2^15 = 2^16
Number of distinct -bit integers in sign magnitude representation (Y)
To find the number of distinct -bit integers in sign magnitude representation, we need to consider the range of values that can be represented using -bit sign magnitude representation.
Range of sign magnitude representation
In sign magnitude representation, the leftmost bit (MSB) is reserved for sign, and the remaining bits represent the magnitude of the number. The MSB is 0 for positive numbers and 1 for negative numbers.
For an -bit representation, the MSB can be either 0 or 1, giving us two possibilities. The remaining bits can represent values from 0 to 2^(-1+2-1) (since the MSB is reserved for sign). Therefore, the total number of distinct -bit integers in sign magnitude representation is:
Y = 2 * 2^(-1+2-1) = 2^0 = 1
Conclusion: X Y = 2^16 * 1 = 2^16 = 1
The product of X and Y is 1, which means that the number of distinct 16-bit integers in 2's complement representation is equal to the number of distinct -bit integers in sign magnitude representation.
To find the number of distinct 16-bit integers in 2's complement representation, we need to consider the range of values that can be represented using 16 bits in 2's complement.
Range of 2's complement representation
In 2's complement representation, the leftmost bit (MSB) is reserved for sign, and the remaining bits represent the magnitude of the number. The MSB is 0 for positive numbers and 1 for negative numbers.
For a 16-bit representation, the MSB can be either 0 or 1, giving us two possibilities. The remaining 15 bits can represent values from 0 to 2^15-1 (since the MSB is reserved for sign). Therefore, the total number of distinct 16-bit integers in 2's complement representation is:
X = 2 * 2^15 = 2^16
Number of distinct -bit integers in sign magnitude representation (Y)
To find the number of distinct -bit integers in sign magnitude representation, we need to consider the range of values that can be represented using -bit sign magnitude representation.
Range of sign magnitude representation
In sign magnitude representation, the leftmost bit (MSB) is reserved for sign, and the remaining bits represent the magnitude of the number. The MSB is 0 for positive numbers and 1 for negative numbers.
For an -bit representation, the MSB can be either 0 or 1, giving us two possibilities. The remaining bits can represent values from 0 to 2^(-1+2-1) (since the MSB is reserved for sign). Therefore, the total number of distinct -bit integers in sign magnitude representation is:
Y = 2 * 2^(-1+2-1) = 2^0 = 1
Conclusion: X Y = 2^16 * 1 = 2^16 = 1
The product of X and Y is 1, which means that the number of distinct 16-bit integers in 2's complement representation is equal to the number of distinct -bit integers in sign magnitude representation.
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Let X be the number of distinct 16-bit integers in 2`s complement representation. Let Ybe the number of distinct -bit integers in sign magnitude representation Then X Y is______.Correct answer is '1'. Can you explain this answer?
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