Consider the following IEEE 754 32-bit floating point value:01001111 01001000 00000000 00000000Enter S, its sign, as either + or -. Enter E, its exponent part's value, in base 10. Enter F, its fraction part's value, in base 10 in the form 0.XXXX where X is a digit
Question
Consider the following IEEE 754 32-bit floating point value:01001111 01001000 00000000 00000000Enter S, its sign, as either + or -. Enter E, its exponent part's value, in base 10. Enter F, its fraction part's value, in base 10 in the form 0.XXXX where X is a digit
Solution
The IEEE 754 32-bit floating point value is broken down as follows:
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The sign bit (S): This is the first bit of the 32-bit number. In this case, it is 0, which means the number is positive. So, S = +.
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The exponent (E): This is the next 8 bits of the 32-bit number. In this case, it is 01001111, which is 79 in base 10. However, the IEEE 754 standard uses a bias of 127 for the exponent, so we subtract 127 from the calculated value to get the actual exponent. So, E = 79 - 127 = -48.
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The fraction (F): This is the remaining 23 bits of the 32-bit number. In this case, it is 01001000 00000000 00000000. To convert this to a decimal, we place a binary point at the left of the number and calculate the value of each bit as a negative power of 2. However, all the bits are 0 except for the second and fifth ones. So, F = 0.5 (for the second bit) + 0.03125 (for the fifth bit) = 0.53125.
So, the sign is +, the exponent is -48, and the fraction is 0.53125.
Similar Questions
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