Fundamentals Of Computer Systems

Problem 9. A floating-point number representation on a certain system has a sign bit, a 4-bit exponent and a 5-bit significand. a) 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 biasing, exponents use two’s complement notation, and exponents of all zeros and all ones are allowed.) b) What bias should be used in the exponent if we prefer all exponents to be nonnegative? Why would you choose this bias? 

Problem 8. Represent the following decimal numbers in binary using 8-bit signed magnitude, one’s complement, two’s complement, and excess-127 representations: a) 31 b) – 31 c) 32 d) – 32