Consider the digital system in the following figure. Combinational logic

$($

with given maximum and

minimum propagation delays

$)$

$$is separated by registers. The registers are edge triggered.

The setup times of register

$1$

$,$

$2$

$$and

$3$

$$are

$16$ns

$,$

$17$ns

and

$18$

$$ns respectively.

a

$.$

$(12$

pt

$)$

$$What is the maximum operating frequency of

this system?

b

$.$

$(12$

pt

$)$

$$If possible, determine the permissible range

for the hold times of the registers.