The following two subproblems are unrelated.

$($a$)$ Compute the value of $\backslash$epsi mach for a normalized floating point system with man$-$

tissa of length $16$ and exponents in the range $6<=$ E $<=6.$

$($b$)$ What is the largest value of k such that fl$(8+2$k$)>$ fl$(8)$ in the IEEE double$-$

precision floating point system? $[$Here fl$($x$)$ denotes the floating point approxi$-$

mation of a number x in R$.]$