Q$5.$ The basic function performed by a computer is execution of a program. A program consists of set of instructions. These instructions are stored in memory in sequential order. The processor reads instructions from memory one at a time and executes them. Consider a hypothetical machine $($representing modern computer$)$ which consists of

$$Program Counter $($PC$)$: A register which contains the address of the memory where the next instruction that is to be executed. This register can store $8-$bit address.

$$Register file: This contains three registers, R$1,$ R$2,$ and R$3$ each capable of storing $8-$bit data.

$$Memory: $256$ X$8$ bits.

$$Sample instructions are:

i$)$AND R$1,$ R$1,$ #$0//$ Clears the register

ii$)$MUL R$1,$ R$2,$ R$3//$ Multiplies the contents of R$2$ and R$3$ and stores the result in R$1$

Answer the following questions:

a$)$ Draw the best hardware implementation for realizing the instruction AND R$1,$ R$1,$ #$0$

b$)$ Consider the instruction MUL R$1,$ R$2,$ R$3.$ What should be the maximum and minimum values of R$2$ and R$3$ to obtain correct output in R$1.$

c$)$Draw the best hardware implementation for realizing the instruction MUL R$1,$ R$2,$ R$3$

d$)$What is the addressability and address space of the given memory.

e$)$ Draw the block diagram for implementing $256$X$8$ bits memory. Show all necessary inputs, outputs and control signals.