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2's complement representation of a 16 bit number (one sign bit and 15 magnitude bit) is FFFF. Its magnitude in decimal representation is
- a)0
- b)1
- c)32676
- d)65, 535
Correct answer is option 'B'. Can you explain this answer?
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2's complement representation of a 16 bit number (one sign bit and 15 ...
Introduction:
In 2's complement representation, the most significant bit (MSB) represents the sign of the number. If the MSB is 0, the number is positive, and if the MSB is 1, the number is negative. The remaining bits represent the magnitude of the number.
Given information:
- The number has a 16-bit representation.
- The 2's complement representation is FFFF.
Analysis:
- The given 2's complement representation is FFFF, which means the MSB is 1 and the remaining bits are all 1s.
- Since the MSB is 1, the number is negative.
- To find the magnitude of the number, we need to convert the remaining bits (all 1s) from binary to decimal.
Conversion from binary to decimal:
- The given number has 15 magnitude bits, which can represent numbers from 0 to 2^15 - 1.
- In this case, all the magnitude bits are 1s, which represents the maximum value for a 15-bit number.
- The maximum value for a 15-bit number is 2^15 - 1 = 32767.
Calculating the magnitude:
- Since the number is negative, the magnitude will be negative as well.
- To calculate the magnitude, we subtract the magnitude value (32767) from 0.
- Magnitude = 0 - 32767 = -32767.
Converting to decimal representation:
- The magnitude of the number is -32767.
- Therefore, the decimal representation of the given 2's complement number is -32767.
Conclusion:
The magnitude of the given 2's complement representation (FFFF) in decimal form is -32767. Therefore, option B (1) is the correct answer.
In 2's complement representation, the most significant bit (MSB) represents the sign of the number. If the MSB is 0, the number is positive, and if the MSB is 1, the number is negative. The remaining bits represent the magnitude of the number.
Given information:
- The number has a 16-bit representation.
- The 2's complement representation is FFFF.
Analysis:
- The given 2's complement representation is FFFF, which means the MSB is 1 and the remaining bits are all 1s.
- Since the MSB is 1, the number is negative.
- To find the magnitude of the number, we need to convert the remaining bits (all 1s) from binary to decimal.
Conversion from binary to decimal:
- The given number has 15 magnitude bits, which can represent numbers from 0 to 2^15 - 1.
- In this case, all the magnitude bits are 1s, which represents the maximum value for a 15-bit number.
- The maximum value for a 15-bit number is 2^15 - 1 = 32767.
Calculating the magnitude:
- Since the number is negative, the magnitude will be negative as well.
- To calculate the magnitude, we subtract the magnitude value (32767) from 0.
- Magnitude = 0 - 32767 = -32767.
Converting to decimal representation:
- The magnitude of the number is -32767.
- Therefore, the decimal representation of the given 2's complement number is -32767.
Conclusion:
The magnitude of the given 2's complement representation (FFFF) in decimal form is -32767. Therefore, option B (1) is the correct answer.
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2's complement representation of a 16 bit number (one sign bit and 15 magnitude bit) is FFFF. Its magnitude in decimal representation isa)0b)1c)32676d)65, 535Correct answer is option 'B'. Can you explain this answer?
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