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If 2's complement representation of a 16-bit number (one-sign bit and 15 Magnitude bits) is FFFF, then its magnitude in decimal representation is ____
Correct answer is '1'. Can you explain this answer?
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If 2s complement representation of a 16-bit number (one-sign bit and 1...
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If 2s complement representation of a 16-bit number (one-sign bit and 1...
Solution:
Given, 2s complement representation of a 16-bit number is FFFF.
2s complement representation of a number is obtained by taking the 1s complement of the number and adding 1 to it.
The 1s complement of FFFF is 0000.
Adding 1 to 0000, we get 0001.
Therefore, the decimal representation of the given 2s complement number is 1.
Explanation:
To understand how the given 2s complement number is converted to decimal representation, we need to understand the concept of 2s complement representation.
2s complement representation is a method of representing both positive and negative numbers in the binary number system. In this method, the leftmost bit is used as a sign bit, where 0 represents a positive number and 1 represents a negative number. The rest of the bits represent the magnitude of the number.
To convert a negative number in 2s complement representation to decimal representation, we need to follow the below steps:
1. Take the 1s complement of the number by flipping all the bits (0s to 1s and vice versa).
2. Add 1 to the 1s complement to get the 2s complement representation.
3. Convert the 2s complement representation to decimal representation.
In the given question, the 2s complement representation of the number is FFFF.
1. Taking the 1s complement of FFFF by flipping all the bits, we get 0000.
2. Adding 1 to 0000, we get 0001.
3. Converting 0001 to decimal representation, we get 1.
Therefore, the magnitude of the given 2s complement number in decimal representation is 1.
Given, 2s complement representation of a 16-bit number is FFFF.
2s complement representation of a number is obtained by taking the 1s complement of the number and adding 1 to it.
The 1s complement of FFFF is 0000.
Adding 1 to 0000, we get 0001.
Therefore, the decimal representation of the given 2s complement number is 1.
Explanation:
To understand how the given 2s complement number is converted to decimal representation, we need to understand the concept of 2s complement representation.
2s complement representation is a method of representing both positive and negative numbers in the binary number system. In this method, the leftmost bit is used as a sign bit, where 0 represents a positive number and 1 represents a negative number. The rest of the bits represent the magnitude of the number.
To convert a negative number in 2s complement representation to decimal representation, we need to follow the below steps:
1. Take the 1s complement of the number by flipping all the bits (0s to 1s and vice versa).
2. Add 1 to the 1s complement to get the 2s complement representation.
3. Convert the 2s complement representation to decimal representation.
In the given question, the 2s complement representation of the number is FFFF.
1. Taking the 1s complement of FFFF by flipping all the bits, we get 0000.
2. Adding 1 to 0000, we get 0001.
3. Converting 0001 to decimal representation, we get 1.
Therefore, the magnitude of the given 2s complement number in decimal representation is 1.
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If 2s complement representation of a 16-bit number (one-sign bit and 15 Magnitude bits) is FFFF,then its magnitude in decimal representation is ____Correct answer is '1'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about If 2s complement representation of a 16-bit number (one-sign bit and 15 Magnitude bits) is FFFF,then its magnitude in decimal representation is ____Correct answer is '1'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 2s complement representation of a 16-bit number (one-sign bit and 15 Magnitude bits) is FFFF,then its magnitude in decimal representation is ____Correct answer is '1'. Can you explain this answer?.
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