Base twelve requires of course twelve digits for the amounts zero through eleven. We don't have any digits to represent ten and eleven so we'll do what the computer scientists (somewhat unimaginatively) did with hexadecimal and use letters instead, so A₁₂ is ten and B₁₂ is eleven.

But what's twelve in base twelve? 10₁₂ of course! It follows exactly the same mechanism of returning the column to zero and incrementing the next one along. So 100₁₂ is twelve times twelve (one hundred and forty four).

Recall the powers from bases:

• 10 = 10¹
• 100 = 10²
• 1000 = 10³

By definition, this is true regardless of what base we're working in. "100" just means a different quantity in each case.

The important thing to remember is that these series of digits are just a way of writing down a particular quantity. The quantity "thirty six" is still the same number of things whether it's 30₁₂ or 36₁₀. The base of the numbering system is an agreed on standard and the lens and language with which we see and express numbers.

Let's look at some basic arithmetic in base twelve...