浮点二进制表示中的混淆

Question

I have tried to output following but got confused,

    float f=3.4;
    char *cp;
    cp=(char *)&f;
    printf("%d\n",*cp);

normalized number I have calculated IEEE 754 std is,

0 10000000 10110011001100110011001

that's why I assumed at cp now value has,

10011001

after convert to 2's complement,

01100111

It should output -103 , but I got -102 in my bloodshed/DevC. why such output???

Answer 1

That's because f is being rounded up:

3.4 = 10110011001100110011001 100110011001...  (repeating 1001)

rounds up to:

3.4 = 10110011001100110011010
                            ^

when stored into single-precision floating-point.

Now when you extract out the last 8 bits, you're actually getting 10011010 instead of 10011001 .

Converting 10011010 -> -102 instead of -103 .

Answer 2

I think you miscalculated:

Prelude> decodeFloat (3.4 :: Float)
(14260634,-22)
(0.03 secs, 2929112 bytes)
Prelude> Numeric.showHex (fst it) ""
"d9999a"

The mantissa ends in 1010 .