What are bases?

Bases are like number systems that help us count and do math using different groups of numbers.

Imagine you have a bag of candies, and you want to share them with your friends. If you use base 10 (which is the one we usually use), you group the candies in tens, just like how we count on our fingers. But what if you had only four fingers on each hand? Then you might use base 4 instead, grouping candies in fours.

In base 10, the numbers go from 0 to 9, and then we add a new digit for every group of ten, that’s why we write "10" when we have ten candies. In base 2, like how computers count, you only use two digits: 0 and 1. It’s like having a light switch, on or off.

Take 13 candies. If you’re using base 10, that’s one group of ten and three left over, so it's "13." But in base 2, you need to count how many groups of two you can make, it becomes "1101" because it breaks down like this:

• 8 candies (which is 2 x 2 x 2)
• 4 candies (which is 2 x 2)
• 1 candy

So, 8 + 4 + 1 = 13 in base 10, and "1101" in base 2. Cool, right?