C Programming - Floating Point Issues - Discussion

Thanks for clear explanation.

5.375

5 --> 101

0.375 * 2 = 0.75
0.75 * 2 = 1.5
0.5 * 2 = 1.0

Consider,only the decimal part from top to bottom ( 0 1 1)
THEREFORE, 5.375=101.011...congrats to surya.......this is d right way......

Why we multiply decimal value *2 ?

Because they asked binary equivalent thats why we multiply by 2 .

Convert decimal to binary(divide decimal number by 2)
->5/2 quotient=2 remainder=1
->2/2 quotient=1 remainder=0
->1/2 quotient=0 remainder=1
In decimal numbers take remainders from bottom to top so binary equivalent of decimal no 5 is 101
Then take fractional part.Here we can convert fractional no to binary by multiply it by 2
So,->0.375*2=0.750 decimal part=0
->0.750*2=1.50 decimal part=1(omit decimal part)
->0.5*2=1.0 decimal part=1
Here we take decimal part from top to bottom.So binary equivalent of 0.375 is 011
Finally 5.375->101.011

I did'tunderstand this can please provide a better solution.

Why should we write only the decimal part from botom to top, it seems some more explanation is need to be there.

In decimal numbers, the digits have values that are powers of ten. Starting at the implied decimal point and working to the left, the number 403 is equal to:
3 x 100 + 0 x 101 + 4 x 102 = 3x1 + 0x10 + 4x100 = 3 + 0 + 400

In binary, the digits have values that are powers of two. Working to the left as before, the number 101 is equal to:
1 x 20 + 0 x 21 + 1 x 22 = 1x1 + 0x2+ 1x4 = (in decimal) 1 + 0 + 4 = 5
So, 1111 1111 = 1x1 + 1x2 + 1x4 + 1x8 + 1x16 + 1x32 + 1x64 + 1x128 = 255.

This also works to the right of the decimal point, but the powers of two are negative (i.e., fractions), so 101.011 in binary is:
1x1/8 + 1x1/4 + 0x1/2 + 1x1 + 0x2 + 1x4 = 5.375

Where the first digit to the right of the decimal point is 2-1 (one-half, or 1/2), the next is 2-2 (1/4), then 2-3 (1/8), etc.

@surya.

Your explanation is nice one.

Thank you surya.