Decimal fraction to binary converter

Decimal to Binary Converter Use this online converter to easily convert decimals to binary numbers. Convert decimal to binary. Share converter:. Embed this tool! This is a decimal to binary and binary to decimal converter.

Conversion is implemented with arbitrary-precision arithmetic , which gives the converter its ability to convert numbers bigger than those that can fit in standard computer word sizes like 32 or 64 bits. Besides the converted result, the number of digits in both the original and converted numbers is displayed.

For example, when converting decimal This means that the decimal input has 2 digits in its integer part and 3 digits in its fractional part, and the binary output has 6 digits in its integer part and 3 digits in its fractional part. To convert binary integer to decimal, start from the left. Take your current total, multiply it by two and add the current digit.

Continue until there are no more digits left. Here is an example of such conversion using the fraction To convert binary fraction to decimal, start from the right with the total of 0. Take your current total, add the current digit and divide the result by 2. There you have 4 simple algorithms that will allow you to convert binary numbers to decimal and back. The key to understanding why those algorithms work is a base-q expansion of a number.

An integer number in any numeric system can be represented in the following form:. Throughout this article this form is referred to as base q expansion of the number N , or simply base q expansion. For the number 0. As it turns out, we can use this base-q expansion form to convert a number from decimal to binary system.

The first thing we need to notice here is all summands except for the last one will be even numbers, because they all are multiples of two. Here we have number 12 which is even, so x0 is zero. Next, we need to find the value for the x1. Since all summands from x1 to xN are multiples of two, we can factor out 2 to single out x1. So, we can write our first step as:. We can write out the polynomial inside the parenthesis as a separate statement:. Here, applying the same logic from above we can see that x1 is equal to 0.

Now, we can see a pattern. Python3 program to convert fractional. Function to convert decimal to binary. Fetch the integral part of. Fetch the fractional part. Conversion of integral part to. Append 0 in binary. Reverse string to get original. Append point before conversion. Conversion of fractional part. Find next bit in fraction. This code is contributed by Ryuga.