'What is the scientific calculation method of 0xf.ap+11 hexadecimal to decimal?

Your similar hex ox2ab, aef97, etc, I understand its scientific notation, but 0xf.ap+11 makes me wonder.Can anyone help me, thanks!

hexhexdump


Solution 1:[1]

It is the hexadecimal floating-point representation available with C99.

The significant portion 0xf.a is expressed in the way each digit has the power of 16 according to the position:

0xf.a = 0xf (= 15 * 16^0) + 0x.a (= 10 * 16^-1)
      = 15 + 10 / 15

while the exponent portion indicates the power of two:

p+11 = 2^11

then

0xf.ap+11 = (15 + 10 / 16) * 2048
          = 30720 + 1280
          = 32000

In actual C code you can say something like:

int main()
{
    double x = 0xf.ap+11;
    printf("%f\n", x);          // it will print 32000.000000

    double y = 32000.0;
    printf("%a\n", y);          // it will print 0x1.f4p+14

    return 0;
}

You'll find the both 0xf.ap+11 and 0x1.f4p+14 are equal to 32000.0. It looks surprising two different expression have the identical numbers.

Sources

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Source: Stack Overflow

Solution Source
Solution 1 tshiono

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