Iam learning floating point representation.I have two doubts, plz help,

1)0 10010011 10100010000000000000000 = 1.1010001 * 2 exp 20 = 1.638125 * 2 exp 23

Here 1010001 is mantissa part and 20 is exponent part , so 1.1010001 * 2 exp 20 but how this is equal to 1.638125 * 2 exp 23 . And also we need in decimal but 1.638125 * 2 exp 23 instead 1.638125 * 10 exp 23 .
How i interpreted is
1.1010001 * 2 exp 20 = 11010001 * 2 exp 13 = 209 * 2 exp 13 or 209 * 10 exp 13?
iam confused...


2) how 1.11....1(23 1's) = (2-2 exp(-23)) ?

you have the fp number: 0 10010011 10100010000000000000000

it is 00 00 D1 49 in memory...

here we have a single-precision value. as you figured out, the exponent is:
10010011b = 147-(biasing constant which is 127) = 20.
10100010000000000000000 - is a real part of the number, so to convert it to decimal you do:
1*(2^-1)+0+1*2(^-3)+0+0+0+1*2(^-7) = 0.5+0.125+0.0078125 = 0.6328125.
so, you've got your number: 1.6328125 * 2^20 = 1712128

thanks zhak.

Hey read Intel Docs and you'll have to never ask such trivial questions.

m, even well organized documentation is not always clear, especially for newbies.

this may also help http://babbage.cs.qc.edu/IEEE-754/