## The color clock’s number system is base 4

We’re all used to the base 10 system, and you might have heard of binary (base 2), which is what computers use. The ‘base’ of a number system actually signifies the value that each digit gets multiplied by when you move from right to left.

So, in base 10, the first digit only counts up to 9. And then the second digit is actually multiplied by 10. The third digit by 100 and so on. This is second nature for us and we don’t even think about it day to day. But when you change from base 10 into a different base, it gets a bit more confusing.

In this clock we use base 4. If we want to represent the number 14, first in base 10 it looks like this:

*14*

* 1 4*

= (10 x 1) + (1 x 4)

= 14

Pretty straightforward, it looks the same, because that’s what we’re used to.

But in base 4:

** 32**

* 3 2*

= (4 x 3) + (1 x 2)

= 14

In base 4, the number 14 actually looks like “32“. The left digit’s value has been multiplied by 4 instead of 10. But the right digit is still multiplied by 1 as it is in all bases. In clock colors, 32 would be “yellow, blue”.

**You don’t really need to remember the above if you don’t want to.** All you need to do is remember which hour or minute value the colors in each place correspond to. The very first diagram explains this. The numerical base explanation is just a more thorough guide.