After seeing such complicated posts on the Internet, I decided to simplify things and write this brief guide to convert any decimal number to a binary number (which is base 2).

Let’s take the example, a decimal number 219.

Steps to convert to decimal:

1) Take the largest number of the power of 2, in this case 2^{7 }and subtract it from 219. You will get a remainder of 91.

2) Repeat step one, now taking the new remainder as the base number. You will obtain a remainder of 27 after subtracting 2^{6}.

3) Repeating for 27, we get a remainder of 11 after subtracting 2^{4}.

4) For 11, we get a remainder of 3 after subtracting 2^{3}.

5) For 3, we get a remainder of 1 after subtracting 2^{1}.

6) For the remainder of 1, note that 1 = 2^{0}.

7) Now we are ready to get our binary number. We will have 8 digit places to fill (note that counting starts from 0). For each power of 2 you have utilised in the above steps, put a ‘1’ into the corresponding digit place.

1 |
1 |
0 |
1 |
1 |
0 |
1 |
1 |

That’s it. Voila! We have 219 converted into our binary number: 11011011

And of course the reverse process will get you the decimal number, that is: 2^{7} + 2^{6} + 2^{4 }+ 2^{3} + 2^{1} + 2^{0 }= 219

Please do leave your comments or suggestions below! Thanks.