Binary Numbers

A binary number is a number, just like the numbers we know and love, only it’s constructed using a base-2 system instead of our traditional base-10. Our base-10, or decimal, system has 10 possible values (0-9), and binary only has 2 (0 or 1). Base-2, or binary, is the language of computers. To understand a little more about why this is, check out this video.

It can be tricky to wrap your head around base-(something other than 10), but it’s important to know that the place values of a base-n system come in powers of n. This means that base-10 has a 1s place (10^0), a 10s place (10^1), a 100s place (10^2), and so on. This means that the furthest right digit of a binary number is the 1s place (2^0), then the 2s place (2^1), then the 4s place (2^2), then the 8s place (2^3), and so on. (If you are feeling like reviewing your powers of 2, now may be a good time to do that - it’s crucial to know them, or at least the first 10).

An easy way to see the connection between decimal numbers and base-10 is to sum each place value that is holding a 1 in the binary number. If the 16s place is 1 (sometimes called “on” because binary 1s and 0s represent transistors that either allow electricity or stop it), then 16 is added to the total. To put it all together, to convert the binary number 11011 to decimal: 1 in the 1s place so add 1, 1 in the 2s place so add 2, 0 in the 4s place, 1 in the 8s place so add 8, and 1 in the 16s place so add 16. The number is then 1 + 2 + 8 + 16 = 27. Decimal 27 is binary 11011.

To get another explanation and learn more, we recommend checking out this article.