Consider the finite floating point decimal system F with bas

Consider the finite floating point decimal system F with base beta = 10 and x = plusminus0.d_1d_2 Times 10^, 1 d_1 9, 0 d_2 9, -1 e 1 for any 0 x F. (a) How many floating point numbers are in F (including 0)? (b) Determine the largest and smallest positive numbers in F. (c) Determine the machine precision (unit roundoff) mu.

Solution

a) The number of floating Point numbers will be 100 i.e. 00 to 99 for each number i.e. 0,1,2...,9

Hence the number of floating Point numbers = 100 * 10 = 1000 (if you are considering .00 also as floating number)

otherwise the number of floating point numbers will be 1000 - 10 = 990

b) The largest floating point number will be 9.99

smallest floating point number will be 0.01

c) The machine precision is of 0.01, i.e. the step size is equal to 1/100