How can we count in base eleven?

Question

We work in base 10. We know base 3 would count 1, 2, 10, 11, 12, 20. How would we count in base 11?

Answer 1

Use the symbol "A" to represent 10. So you get $1,2,3,4,5,6,7,8,9,A,10,11,12,13,14,15,16,17,18,19,1A,20,\dots$

Answer 2

You would have to add a symbol for $10$, such as $A$. Then it would be $$\begin{array}{|c|c|c|c|c|c|c|} \hline \text{Base 10} & 1 & 2 & 3 & \dots & 9 & 10 & 11 \\ \hline \text{Base 11} & 1 & 2 & 3 & \dots & 9 & A & 10 \\ \hline \end{array}$$

Answer 3

You know how counting in Hexadecimal is done right? It could be done similarly with just the A included.Leave out the other alphabets.

Answer 4

Typically one would write a special symbol that represents ten, say, $A$. Then, the first few natural numbers in base eleven would be written as

$$0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 20, 21$$

and so on. In this system,

• the quantity one hundred would be written as $91$,

• the quantity one hundred and nine would be written as $9A$, and

• the quantity one hundred ten would be written as $A0$,

• the quantity one hundred twenty would be written as $AA$, and

• the quantity one hundred twenty-one would be written as $100$.

Answer 5

base $2$ we only have two digits $0,1$

base $10$ we have $10$ digits $0,1,2,3,4,5,6,7,8,9$

base $11$ we would have $11$ digits $0,1,2,3,4,5,6,7,8,9,\beta$

where $\beta$ is a new digit