In this practice, we want to convert a 32-bit integer to IEEE 754 32-bit floating point

representation. The goal is to obtain sign bit, exponent, and fraction from an integer number.

Finding sign bit is very trivial, sign bit is 1 if number is negative, and 0 otherwise. Below I explain

hints on how to find exponent and fraction.

To find the exponent and fraction, we should convert an integer number into normalized

scientific format. For example:

1101 should be converted into 1.101 x 2

3

In general, we need to convert the number into 1.F x 2

E

representation. But how do we find

the normalized representations? Given a 32-bit normalized number, for example:

0000 0000 0000 0000 0000 0010 1000 1000

the key is to find the first none-zero bit from the left. This bit is the none-zero bit of the

normalized representation. For example, in the number above, bit at significance 2^9 is the

none-zero bit.

How you find this bit? I leave it up to you and your team to discuss best strategy

,

but when you find this bit, you have the normalized representation. How? In the normalized

representation formula:

1.F x 2

E

Where

E

is the significance of the number you found, 9 in our example. And

F

is all the bits on

the right side of it, 010001000 in our example. So the normalized representation of the number

above is

1.00010001000 x 2

9

Now that you have the normalized representation, you can extract exponent and fraction:

fraction = F = 00010001000

exponent = 127 + E = 127 + 9 = 136

Practice

Develop a C++ program to convert an integer to 32-bit floating point representation. Print

sign, exponent, and fraction and the end of your program.