Design a datapath and a control unit for the following instructions:

add R$1,$ R$2,$ R$3$ # R$1=$R$2+$R$3$

addi R$1,$ R$2,7-$bits$-$data # R$1=$R$2+$data

lw R$1,$ memaddress # R$1=$ Memory$($memaddress$)$

jump R$1,$ memaddress # Jump to location: Memory$($memaddress$)+$ R$1$

beq R$1,$ R$2,7-$bits$-$data # if R$1=$R$2$ then jump to PC$+2+$data

Assume each instruction has $16$ bits. Also assume that there are $8$

registers, an instruction memory unit with $1$K bytes, and a data memory

unit with $1$K bytes.

a$)$ Define a format for each instruction.

b$)$ Draw a datapath which is able to perform the above operations; be sure to include IR$,$ Register File, ALU, Memory Unit, PC$,$ control signals, number of wires from one component to the other, and any other components that you may need. Write any assumption that you make.

c$)$ Design the control unit and draw the minimized logic diagram for it$.$