Around 250 B.C.,the Greek mathematician Archimedes proved that 223/71< Pi <22/7

Question

Around 250 B.C.,the Greek mathematician Archimedes proved that 223/71< Pi <22/7 ,Had he had access to a computer and the standard library he would have been able to determine that the single-precision floating-point approximation of pi has the hexadecimal representation Ox40490FDB. Of course, all of these are just approximations, since pi is not rational.

A. What is the fractional binary number denoted by this floating-point value?
B. What is the fractional binary representation of 22/7?
C. At what bit position.( relative to the binary point) do these two approximations
to pi diverge?

Explanation / Answer

A) Answer :

The given fractional floating point number is

Ox40490FDB

Actually the pi value represented in hexadecimal number in single-precision floating point is 3.243F6A8885A3

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