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The decimal number 0.239 x 213 has the following hexadecimal representation (without normalization and rounding off:
- a)0D 24
- b)0D 4D
- c)4D 0D
- d)4D 3D
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The decimal number 0.239 x 213 has the following hexadecimal represent...
The decimal number is 0.239 x 213
We have to find hexadecimal representation without normalization.
Biased exponent = 13 + 64 = 77
Representing 77 in binary (77)10 = (1001101)2
Representing mantissa in binary
senting mantissa in binary (0.239)10 = 0.00111101000101
We have to find hexadecimal representation without normalization.
Biased exponent = 13 + 64 = 77
Representing 77 in binary (77)10 = (1001101)2
Representing mantissa in binary
senting mantissa in binary (0.239)10 = 0.00111101000101
Most Upvoted Answer
The decimal number 0.239 x 213 has the following hexadecimal represent...
The given decimal number is 0.239 multiplied by 213. We need to find its hexadecimal representation without normalization and rounding off.
To solve this problem, we will follow the steps below:
1. Multiply the decimal number by 213:
0.239 * 213 = 51.007
2. Convert the integer part of the result to hexadecimal:
51 (in decimal) = 33 (in hexadecimal)
3. Convert the fractional part of the result to hexadecimal:
To convert the fractional part, we will multiply it by 16 repeatedly and take the integer part at each step until we get zero or the desired precision.
0.007 * 16 = 0.112
0.112 * 16 = 1.792
0.792 * 16 = 12.672
4. Combine the hexadecimal representations of the integer and fractional parts:
The integer part is 33, which is represented as 21 in hexadecimal.
The fractional part is 0.112, which is represented as 0.1 in hexadecimal.
Therefore, the hexadecimal representation of the decimal number 0.239 * 213 is 21.1.
5. Rearrange the digits to match the given options:
The given options are:
a) 0D 24
b) 0D 4D
c) 4D 0D
d) 4D 3D
Among these options, option d) 4D 3D matches the hexadecimal representation we found in step 4, which is 21.1. Therefore, the correct answer is option d) 4D 3D.
By following these steps, we have determined that the hexadecimal representation of the decimal number 0.239 * 213 is 4D 3D.
To solve this problem, we will follow the steps below:
1. Multiply the decimal number by 213:
0.239 * 213 = 51.007
2. Convert the integer part of the result to hexadecimal:
51 (in decimal) = 33 (in hexadecimal)
3. Convert the fractional part of the result to hexadecimal:
To convert the fractional part, we will multiply it by 16 repeatedly and take the integer part at each step until we get zero or the desired precision.
0.007 * 16 = 0.112
0.112 * 16 = 1.792
0.792 * 16 = 12.672
4. Combine the hexadecimal representations of the integer and fractional parts:
The integer part is 33, which is represented as 21 in hexadecimal.
The fractional part is 0.112, which is represented as 0.1 in hexadecimal.
Therefore, the hexadecimal representation of the decimal number 0.239 * 213 is 21.1.
5. Rearrange the digits to match the given options:
The given options are:
a) 0D 24
b) 0D 4D
c) 4D 0D
d) 4D 3D
Among these options, option d) 4D 3D matches the hexadecimal representation we found in step 4, which is 21.1. Therefore, the correct answer is option d) 4D 3D.
By following these steps, we have determined that the hexadecimal representation of the decimal number 0.239 * 213 is 4D 3D.
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The decimal number 0.239 x 213 has the following hexadecimal representation (without normalization and rounding off:a)0D 24b)0D 4Dc)4D 0Dd)4D 3DCorrect answer is option 'D'. Can you explain this answer?
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