(a) 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 Zebronian 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). How many bits will you need to represent each character if you want to use the minimum number of bits? [5 marks]

(b) If the floating-point number representation on a certain system has a sign bit, a 3-bit exponent and a 4-bit significand:

(i) What is the largest positive and the smallest positive number that can be stored on this system if the storage is normalized? (Assume no bits are implied, there is no bias, exponents use two's complement notation, and exponents of all zeros and all ones are allowed.) [5 marks]

(ii) What bias should be used in the exponent if we prefer all exponents to be non-negative? [2 marks]

(c) Hex value 0xC29C3480 represents an IEEE-754 single-precision (32 bit) floating-point number. Work out the equivalent decimal number. Show all workings (e.g. converting exponent and mantissa). [8 marks]