Representing (0.5)in IEEE754 format

Dimitri

Ok so this is what my notes tell me..

• Example: Show the IEEE 754 binary
representatoin of the number 0.5 in single percision
• This is equivalent to 1.0 × 2−1 in normalised
binary scientific notation
• Thus, the fraction is 00000 . . . 000 (i.e. we
ignore the “1.” in the significand)
• The sign is positive, which is 0
• The exponent is
−1 + 127 = 12610 = 011111102
• We can now put it all together
An Example Conversion
• Thus the IEEE floating-point formatted number
for 0.510 is
00111111000000000000000000000000
which, formatted differently, is
0011 1111 0000 0000 0000 0000 0000 0000
• We can also express this as
3F00000016
• Also, 0.5, 1.0 and 1.5 are represented
in hexadecimal as 3F000000, 3F800000,
3FC00000, respectively.

What i can't understand is how you get the fraction if anyone can help it would be greatly appreciated
Cheers
Gav

pan

The basic algorithm is:
to convert fractional part, repeatly multiply the fractional part by 2
and note the whole part until zero is reached.

E.g. 5.8125 Fractional decimal number (base 10)
the integer 5 = 101 in binary (easy part)

For the fractional part 0.8125
2*0.8125 = 1.625 keep the 1 and use the 0.625
2*0.625 = 1.25 keep the 1 and use the 0.25
2*0.25 = 0.5 keep the 0 and use the 0.5
2*0.5 = 1.0 keep the 1 and use the 0.0
2*0.0 = 0.0 keep the 0 and use the 0.0
etc... for the required number of fractional bits (e.g mantissa should 23 bits long for IEEE 754)

put it together
101.1101000000000000... a fractional binary number

Good luck!

pan

Dimitri

Ah, thanks the penny has finally dropped cheers pan much appreciated!

Newb

I wrote this to demonstrate:
http://www.tuxpages.com/math/ieee754.shtml

Newb

And the reverse:
http://www.tuxpages.com/math/ieee754todec.shtml