# High Level Math Question!

Hey arduinians,

I was working on a keypad one day when i came up with my own math problem that I could not solve!

Keypads are 0-9, I was trying to figure out the least number of digital pins needed using the on/off method rather than the resister/analog method.

I call this method, the and-gate-method.
(Someone probably came up with it already)

To confuse us less, lets say the keypad is A-Z and the numbers are digital pins.
with 1 pin i can have 1 letter
with 2 pins i can have 3 letters
with 3 pins i can have 7 letters
with 4 pins i can have 15 letters!

Confused? Example (3 pins):

A=1
B=2
C=3
D=1+2
E=1+3
F=2+3
G=1+2+3

The Ultimate Math question you’ve been waiting for!
What is the formula?
X represents digital pins
Y represents letters

Is this not just binary arithmetic?

Number of button states (2 - on/off), raised to the power of (number of pins),

maybe -1, I haven’t thought this bit through much yet.

That is only if you want to be able to press one button at a time of course.
If the above is garbage please ignore it

It seems you are correct!

This might be useful for anyone trying to do something using the least amount of wires. (keypads…).

Given n wires you can have them in 2n different states.

So with 4 wires you can have 16 states. You have to reserve a state for “nothing pressed” so you get
2n -1 keys