I E E E    S T A N D A R D    F L O A T I N G    P O I N T     F O R M A T
                                Carter Bays  11/96

Most computers manufactured after 1990 utilize IEEE floating point format,
which is described below.   Single ("float") objects are 32 bits:
                   seee eeee efff ffff ffff ffff ffff ffff
"Double" objects are 64 bits:
   seee eeee eeee ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff
where:  s = sign of fraction (as signed magnitude, not two's compliment)
        e = exponent (as a nine bit bit integer, two's complement form,
            where zero exponent is represented as 01111111, or "excess 127")
        f = fraction bits (since all numbers can be represented as
            1.ffffff . . . ,    we strip off the leading "1", which
            the machine hardware adds back before any calculation)
or, put another way, given the internal format: sEF (with E,F = e...e,  f...f)
then:          (float) N  = (-1)^s * 2^(E-127) * (1.F)
(see J. P. Hayes, "Computer Organization and Architecture")

Here are some easy steps to convert to floating point ("float", or 32 bit)

1) Find the binary value
        1/3   = .01010101010 . . .
        1 1/3 = 1.0101010101 . . .
        17    = 10001.000000 . . .
        40.75 = 101000.11000 . . .

2) convert to "1. . . ."  times 2^e
        1/3   = 1.01010101 . . . times 2^(-2)
        1 1/3 = 1.01010101 . . . times 2^0
        17    = 1.00010000 . . . times 2^4
        40.75 = 1.01000110 . . . times 2^5

3) strip off the "1."  This is "F"
        1/3    F = 010101010 . . .
        1 1/3  F = 010101010 . . .
        17     F = 000100000 . . .
        40.75  F = 010001100 . . .

4) Calculate the exponent,  "E"
   as:  01111111 + eeeeeeee     ( e...e below is expressed as decimal number )
        1/3   -> 01111111 + (-2)  = 01111101
        1 1/3 -> 01111111 + 0     = 01111111
        17    -> 01111111 + 4     = 10000011
        40.75 -> 01111111 + 5     = 10000100

5) Concatenate  s,  E,  and F,  getting sEF (for examples given,  s=0 -> "+")
        1/3   = 00111110101010101010 . . .
        1 1/3 = 00111111101010101010 . . .
        17    = 01000001100010000000 . . .
        40.75 = 01000010001000110000 . . .

6) Convert to hexadecimal
        1/3   = 3eaaaaab (last bit rounded up)
        1 1/3 = 3faaaaab
        17    = 41880000
        40.75 = 42230000

7) If a number is negative, the first bit, s,  is the sign of F and is set to 1
        - 1/3 = beaaaaab
        -17   = c1880000


To convert from "float" to a decimal number, perform steps 1 - 7 in reverse order.
(i.e. first determine the sign; then convert from hexadecimal to binary; etc.)