How to convert float number to Binary?

Question

Can anyone please tell me how can I convert this float number: 12.25 to binary? I know how to convert the "12" but not the 0.25

Any help is much appreciated. Thanks

Solution 1

Keep multiplying the number after decimal by 2 till it becomes 1.0:

0.25*2 = 0.50
0.50*2 = 1.00

and the result is in reverse order being .01

Solution 2

Consider below example

Convert 2.625 to binary.

We will consider the integer and fractional part separately.

The integral part is easy, 2 = 10. 

For the fractional part:

0.625   × 2 =   1.25    1   Generate 1 and continue with the rest.
0.25    × 2 =   0.5     0   Generate 0 and continue.
0.5     × 2 =   1.0     1   Generate 1 and nothing remains.

So 0.625 = 0.101, and 2.625 = 10.101.

See this link for more information.

Solution 3

(d means decimal, b means binary)

1. 12.25d is your float.
2. You write 12d in binary and remove it from your float. Only the remainder (.25d) will be left.
3. You write the dot.
4. While the remainder (0.25d) is not zero (and/or you want more digits), multiply it with 2 (-> 0.50d), remove and write the digit left of the dot (0), and continue with the new remainder (.50d).

Solution 4

The float value is stored in IEEE 754 format so we can't convert it directly like integer, char to binary.

But we can convert float to binary through a pointer.

#include <stdio.h>

int main()
{
    float a = 7.5;
    int i;
    int * p;

    p = &a;
    for (i = sizeof(int) * 8 - 1; i >= 0; i--)
    {   
        printf("%d", (*p) >> i & 1); 
    }   

    return 0;
}

Output

0 10000001 11100000000000000000000

Spaces added for clarification, they are not included as part of the program.

Solution 5

x = float(raw_input("enter number between 0 and 1: "))

p = 0
while ((2**p)*x) %1 != 0:
    p += 1
    # print p

    num = int (x * (2 ** p))
    # print num

    result = ''
    if num == 0:
        result = '0'
    while num > 0:
        result = str(num%2) + result
        num = num / 2

    for i in range (p - len(result)):
        result = '0' + result
    result = result[0:-p] + '.' + result[-p:]

print result #this will print result for the decimal portion

View more solutions

Comments

[Rick Regan]

@Slim Black: Beware: that works fine for numbers like 0.25, which have exact representations in binary, but not for numbers like 0.1, which don't: 0.1*2 = 0.2, 0.2*2 = 0.4, 0.4*2 = 0.8, 0.8*2 = 1.6, 0.6*2 = 1.2, 0.2*2 = 0.4, ... It repeats forever, and the result is 0.0(0011) (the part in parentheses repeats).

[Rick Regan]

@Slim Black: And note, to implement this correctly programmatically, you'll need decimal arithmetic -- see my article exploringbinary.com/base-conversion-in-php-using-bcmath, specifically section dec2bin_f() .)

[nautilusvn]

What if my float is 5.1? Doing yours steps, I got into a infinite loop, please help!

[comonad]

@nautilusvn: because there is no power of 2 that is also a multiple of 10, that number has an infinite sequence of digits. you might want to abort your computation somewhere.

[Kin Cheung]

maybe you also want to add the reference to where you got that from. this python code looks familiar to me.

[comonad]

@nautilusvn hm, yes, "while not zero" is a silly statement.. changing that.

[Michi]

I know is old, but What's the value of i here?

[Michi]

Me I’m fine, I think you need to replace it into your Answer:))

[Krzysztof Madej]

Hi. Welcome on SO. Thank you for your code, but can you explain a bit how it solves the issue?