Explain converting decimal fraction to binary

Explain converting decimal fraction to binary step  by step

Suppose you want to convert a decimal fraction .625 into binary. Follow the following steps

Step 1: Begin with the decimal fraction and multiply by 2. The whole number part of the result is the first binary digit to the right of the point.

.625 x 2 = 1.25, the first binary digit to the right of the point is a 1.



Step 2: Next we disregard the whole number part of the previous result (the 1 in this case) and multiply by 2 once again. The whole number part of this new result is the second binary digit to the right of the point.

.25 x 2 = 0.50, the second binary digit to the right of the point is a 0.



Step 3: Disregarding the whole number part of the previous result, we multiply by 2 once again. The whole number part of the result is now the next binary digit to the right of the point.

.50 x 2 = 1.00, the third binary digit to the right of the point is a 1.



Step 4: In fact, we do not need a Step 4. We are finished in Step 3, because we had 0 as the fractional part of our result there.

Hence the representation of .625 = .101₂