Fraction Conversion Explained

How do you convert decimal fraction to binary?

Given the decimal fraction 0.2578125, how can you convert it to binary with 8 bits to the right of the binary point?

Binary Conversion Process

To convert a decimal fraction to binary, follow these steps:

Separate into Integer and Fraction Parts

1. Separate the decimal number into its integer and fraction parts. For 0.2578125, the integer part is 0 and the fraction part is 0.2578125.

Convert Integer Part to Binary

2. Convert the integer part (0) to binary, which remains as 0.

Convert Fraction Part to Binary

3. Convert the fraction part (0.2578125) to binary using the multiplication-by-2 method:

a. Multiply the fraction by 2: 0.2578125 x 2 = 0.515625. The integer part (0) is the first binary digit after the binary point.

b. Take the fraction part (0.515625) and multiply it by 2 again: 0.515625 x 2 = 1.03125. The integer part (1) is the second binary digit after the binary point.

c. Repeat this process with the new fraction part (0.03125), and so on, until you have 8 bits to the right of the binary point or the fraction part becomes zero.

4. After performing 8 iterations, we get the following binary digits: 0.01000011.

So, 0.2578125 in binary with 8 bits to the right of the binary point is 0.01000011.