how IEEE-754 floating point numbers work

Posted by hatorade on Stack Overflow See other posts from Stack Overflow or by hatorade
Published on 2010-04-25T01:49:25Z Indexed on 2010/04/25 2:43 UTC
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ieee-754

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Let's say I have this:

float i = 1.5

in binary, this float is represented as:

0 01111111 10000000000000000000000

I broke up the binary to represent the 'signed', 'exponent' and 'fraction' chunks.

What I don't understand is how this represents 1.5.

The exponent is 0 once you subtract the bias (127 - 127), and the fraction part with the implicit leading one is 1.1.

How does 1.1 scaled by nothing = 1.5???

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