First, I'd like to say that an article similar to this has already been written by Joshua Alias-Vigathon. While that article gave the concepts and basics of binary, the goal of this article is to give a little more detail about conversion between the binary and decimal systems. One other thing I should mention is that I don't think this is the “official” method of conversion. This is only a method I came up with that has proved useful for me.

As the name suggests, binary consists of only two numbers: 0 and 1. Coincidentally, the binary system is also based on powers of 2 (i.e. 1, 2, 4, 8, 16, 32, 64, 128 etc.). The system works because every decimal number can be build using those numbers and, if we represent those numbers with 1's and 0', any decimal number can be written using only 1's and 0's. That being said, let's get converting!

For this example, we'll try converting the number 2 into decimal and we'll call the number 2 “n“.

First, start by drawing a horizontal table with two rows. It should look something like this:

The top row is for numbers from the decimal system and the bottom row is for binary numbers.

Next, fill in the top row with powers of 2, going from right to left, starting with the number 1. Your table might look something like this:

Note: The table only has to be as long as the biggest decimal number that can fit into n (the number we're trying to convert into binary), in this case, 2.

For our final step, starting from the biggest number that can fit into n, we fill in a “1” if it fits into our number, and a “0” if it doesn't. Obviously, 128 is much bigger than 2 and cannot fit into it, so under 128 we would put a “0“. The same goes for 64, 32, 16, 8 and 4. 2, however, perfectly fits into 2, so we can write a “1” under the 2. Once we write a “1” under the 2, we would subtract that number from n (n-2 or 2-2), which would leave us with zero. Our last number 1, can't fit into 0, so we would write a “0” under 1. That may have been a little confusing, but if you made it through, you might have something like this:

There, on the bottom row, is our binary equivalent of 2: 00000010. Now, much like the 0's in front of a decimal number don't matter (i.e. 00000002 is the same as 2), the 0's in front of binary numbers don't matter. Instead of writing 00000010 then, our number could simply be written as 10. So the number 2, converted to binary, would be 10.

Let's try one more example, this time, converting the number 35 into binary and again, let's call 35 “n“.

Once again, we start by drawing an empty table and filling the top row with powers of 2, going right to left, starting with 1:

Neither 128 or 64 can fit into 35 so we'd write 0's under both. 32 can fit however, so we can write a “1” under 32. Since we wrote a “1“, take n and subtract 32 (35-32). That leaves us with 3 left over. The numbers 16, 8, and 4 cannot fit into 3, so we write 0's under those. 2 fits into 3 so we write a “1” under 2 and subtract 2 from 3, leaving us with one. Finally, 1 fits into 1 so we can write a “1” under 1. Hopefully, your table looks similar to this:

If so, you've pretty much gotten the hang of it. You should be left with 00100011 or, without the 0's in front, 100011. So 35, in binary would be written as 100011.

If you feel confident about converting to binary or want some more practice, try converting these numbers into binary:

Number - Answer

3 - 11

11 - 1001

31 - 11111

74 - 1001010

200 - 11001000

351 - 101011111

This process will likely be confusing, but don't give up, understanding comes with practice. There are likely many other ways to convert numbers into binary so if this method doesn't work for you, try another. Finally, if you have any questions or suggestions, leave a comment. Thanks for reading this article and happy converting!

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