converting fraction into binary by division

Question

So i have a question regarding converting from farctions into binary decimals.

if i have $\frac{3}{17},\frac{2}{9},\frac{1}{7}$

How can i convert those fraction into binary decimals using divison.

I mean this way: $3:17=$ here i would get an periodic decimal.Need help understand how the principles of "normal" division by hand work in binary system.

Any help would be appreciated.

Answer 1

Presumably you know how to convert integers to decimal by dividing by two and recording the remainders then reversing the order of the remainders. The same process in reverse will work for values less than 1.

So multiple by 2 then record if the value is less than or more than one. Repeat with any fractional part.

Example with $\frac{3}{17}$:

• $\frac{3}{17}\times2=\frac{6}{17}=0+\frac{6}{17}$
• $\frac{6}{17}\times2=\frac{12}{17}=0+\frac{12}{17}$
• $\frac{12}{17}\times2=\frac{24}{17}=1+\frac{7}{17}$
• $\frac{7}{17}\times2=\frac{14}{17}=0+\frac{14}{17}$
• $\frac{14}{17}\times2=\frac{28}{17}=1+\frac{11}{17}$
• $\frac{11}{17}\times2=\frac{22}{17}=1+\frac{5}{17}$
• $\frac{5}{17}\times2=\frac{10}{17}=0+\frac{10}{17}$
• $\frac{10}{17}\times2=\frac{20}{17}=1+\frac{3}{17}$

At this point you can see it is repeating so the answer is: $0.\overline{00101101}$.

The other fractions can be done in a similar fashion.