Let the floating point number representation on a certain system have a sign bit, a 3-bit exponent, and a 4-bit significand.

a) Show how to determine the largest positive and the smallest positive number that can be stored on the system if the storage is normalized. (Assume that no bits are implied, there is no biasing, exponents use two's complement notation, and exponents of all zeros and all ones are allowed).

b) What "standard" bias should be used in the exponent if we prefer not to write negative exponents using two's complement notation. Show the largest positive and the smallest positive number that can be stored on the system using this notation, if the storage is normalized. (Again, assume that no bits are implied and exponents of all zeros and all ones are allowed).