IEE754 - Floating point number representation

Question

I am writing program which takes floating number from input and outputs hex representation of this number.

What I did to solve it was:

1. Divide number to whole and decimal part.
2. Convert whole and decimal parts to binary representation. a) Whole number divided by 2, if number mod2 ==1, add 1, else add 0. Turn whole number around. b) Decimal part is being multiplied by 2, if it's higher than 1, substract 1 and do it again.
3. If number is less than 0, sign is 1, else sign is 0.
4. Get exponent (127+/-x), convert it to binary (whole).
5. Get mantissa.
6. Convert sign+exponent+mantissa to hex.

My program is passing through every test there was on SPOJ forum. I had to look for manual test cases where it fails myself.

So in case of number -123123.2323 I received number:

(hex) c7 f0 79 9d

Binary whole=11110000011110011 Binary decimal=0011101101111000000000 ....

Mantissa=11100000111100110011101

Meanwhile https://www.h-schmidt.net/FloatConverter/IEEE754.html gives me:

Mantissa=11100000111100110011110

How does it work and why this way in that case? Using https://www.rapidtables.com/convert/number/decimal-to-binary.html?x=0.2323 when I convert 0.2323 to binary it gives me 0.0011101101111. I used this part to finish the mantissa after adding whole binary number (-1), up to 23 bits. What am I doing wrong?

Answer 1

Alright so it's not like my program or solution was wrong, just my thought process and I lacked crucial information about floating point numbers.

As Mr. "chux" said, the number I tried to compute (-123123.2323) should be read by computer as other number (-123123.2344). Since I used string for input and simply divided number into whole and decimal parts, I couldn't see floating point numbers limitations.

Solution is to read number as floating point number, let computer change it's value and then read it as string and work with that.