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If 2's complement representation of a 16-bit number (one-sign bit and 15 Magnitude bits) is FFF 1, then its magnitude in decimal representation is ____
Correct answer is '1'. Can you explain this answer?
Verified Answer
If 2's complement representation of a 16-bit number (one-sign bit ...
2's complement number = F F F F.
given that 1 sign bit and 15 magnitude bits.
This question is part of UPSC exam. View all Electronics and Communication Engineering (ECE) courses
Most Upvoted Answer
If 2's complement representation of a 16-bit number (one-sign bit ...
Conversion of 2s Complement to Decimal
To convert a 2s complement representation of a number to decimal, we follow these steps:
1. Determine the sign of the number:
- If the left-most bit is 0, the number is positive.
- If the left-most bit is 1, the number is negative.
2. Find the magnitude of the number:
- If the number is positive, the magnitude is simply the binary value of the remaining bits.
- If the number is negative, we must first invert all the bits and then add 1 to the result. This gives us the magnitude of the number.
3. Multiply the magnitude by the sign:
- If the sign is positive, the result is the magnitude.
- If the sign is negative, the result is the magnitude multiplied by -1.
In this case, the 2s complement representation is FFF1. Let's follow the above steps to convert it to decimal:
1. The left-most bit is 1, so the number is negative.
2. The magnitude is found by inverting all the bits and adding 1:
- FFF1 inverts to 000E.
- Adding 1 gives us 000F.
- So the magnitude is 15.
3. The sign is negative, so the result is the magnitude multiplied by -1:
- 15 x -1 = -15.
Therefore, the magnitude of the given 2s complement representation in decimal form is -15.
To convert a 2s complement representation of a number to decimal, we follow these steps:
1. Determine the sign of the number:
- If the left-most bit is 0, the number is positive.
- If the left-most bit is 1, the number is negative.
2. Find the magnitude of the number:
- If the number is positive, the magnitude is simply the binary value of the remaining bits.
- If the number is negative, we must first invert all the bits and then add 1 to the result. This gives us the magnitude of the number.
3. Multiply the magnitude by the sign:
- If the sign is positive, the result is the magnitude.
- If the sign is negative, the result is the magnitude multiplied by -1.
In this case, the 2s complement representation is FFF1. Let's follow the above steps to convert it to decimal:
1. The left-most bit is 1, so the number is negative.
2. The magnitude is found by inverting all the bits and adding 1:
- FFF1 inverts to 000E.
- Adding 1 gives us 000F.
- So the magnitude is 15.
3. The sign is negative, so the result is the magnitude multiplied by -1:
- 15 x -1 = -15.
Therefore, the magnitude of the given 2s complement representation in decimal form is -15.
Community Answer
If 2's complement representation of a 16-bit number (one-sign bit ...
FFF1 can be written in binary as 1 1111 1111 1111. since the no. is in 2's complete, to find its magnitude we need to again convert it in 2's complement which will be 0 0000 0000 0001. so ans is 1.
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If 2's complement representation of a 16-bit number (one-sign bit and 15 Magnitude bits) is FFF 1,then its magnitude in decimal representation is ____Correct answer is '1'. Can you explain this answer?
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