A single-precision binary float is represented using 32-bits. These bits are divided into three sections to represent the sign, exponent, and fractional parts of a decimal number (according to the IEEE 754 standard).
The fractional part is first converted into a decimal by summing all the s (where is the position of a bit in the fractional part that has a ). For example, if the 23-bit fractional part has a at bit number 2 and 3:
Its decimal equivalent would be:
Applying the following formula will convert the whole 32-bit binary number into a decimal,
,where is the sign-bit, Fraction is the value that has been computed above as an example, and is the numerical value, in base 10, of the 8-bits reserved for the exponent.
Substitute the values in the formula to obtain the final answer:
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