a$)$ Consider a distributed system with $32$ processors and $32$ memory modules which are interconnected using omega switching network with two input two output switch. Answer the following questions.

i$.$ Number of stages in the network $[0\mathrm{.}5$ mark$]$

ii$.$ Number of switches in each stage $[0\mathrm{.}5$ mark$]$

iii. Number of bits needed in the routing tag $[1$ mark$]$

b$)$ Out of four classes of parallel systems under Flynn$$s classification, which class is best suited for applications such as railway reservation systems? $[1$M$]$ c$)$ Having a large number of processor registers makes it possible to reduce the number of memory accesses needed to perform complex tasks. Devise a simple computational task to show the validity of this statement for a processor that has four registers compared to another that has only two registers.$[3$M$]$