You have stumbled on an unknown civilization while sailing around the world. The people, who call themselves Zebronians, do math using 40 separate characters (probably because there are 40 stripes on a zebra). They would very much like to use computers but would need a computer to do the Zebronain math, which would mean a computer that could represent all 40 characters. You are a computer designer and decide to help them. You decide the best thing is to use BCZ, Binary-Coded Zebronian (which is like BCD, except it codes Zebronian, not Decimal). Determine and informally document your thoughts through explanation and justification with respect to the following:

(a) How many bits do you need to represent each character if you want to use the minimum number of bits?

(b) Consider and explain how you might handle basic arithmetic(addition and subtraction) with Binary Coded-Zebronian.