1. In the classes, we discussed three forms of floating number representations as shown below, Lecture Note Form : F = (0.d1d2d3 dm) e , (1) Normalized Form : F = (1.d1d2d3 dm) e , (2) Denormalized Form : F = (0.1d1d2d3 dm) e , , (3) where di , , e Z, 0 di 1 and emin e emax. Now, lets take a system where, = 2, m = 4 and 3 e 6. Based on these, answer the following:

(a) (3 marks) Find how many non-negative numbers in total can be represented by this system? Find this separately for each of the three forms above.

(b) (3 marks) What are the largest/maximum numbers that can be stored in the system for each of the three forms defined above?

(c) (3 marks) What are the non-negative smallest/minimum numbers that can be stored in the system for each of the three forms defined above?

(d) (4 marks) Using Eq.(1), find all the decimal numbers for e = 1, plot them on a real line and show if the number line is equally spaced or not.