$1)(20$ points$)$ Design a minimized state diagram for a sequential circuit of a vending machine

controller. One product, a $$0\mathrm{.}35$ bottle of water $($output W$).$ The vending machine takes only

quarters $($input Q$)$ and dimes $($input D$),$ but refunds nickels $($output C$).$ No other I$/$O signals,

and it uses only a single register $($R for memory$).$ Show the complete state diagram and

state transition table.

$2)(20$ points$)[$Instruction Mix and CPI$]$ Assume that for a given program, $65\%$ of the executed

instructions are ALU, $25\%$ are load$/$store$,$ and $10\%$ are branch.

a$)$ Given this instruction mix and the assumption that an ALU instruction requires $2$ cycles,

a load$/$store instruction takes $6$ cycles, and a branch instruction takes $3$ cycles, find the

effective CPI.

b$)$ For a $20\%$ improvement in performance, how many cycles, on average, may an ALU

instruction take if load$/$store and branch instructions are not improved at all?

$3)(20$ points$)[$ISA Design$]$ Assume that we would like to expand the MIPS register file to $128$

registers and expand the instruction set to contain four times as many instructions.

a$)$ How would this affect the size of each bit field in the ALU $($R$-$type$)$ instructions?

b$)$ How would this affect the size of each bit field in the Memory $($I$-$type$)$ instructions?

$4)(40$ points$)[$Control Range$]$ Suppose the program counter $($PC$)$ is set to $0$x$20000000.$

a$)$ What range of addresses can be reached using the MIPS jump$-$and$-$link $($jal$)$ instruction?

b$)$ How does that change if you increase the number of registers to $64?$

c$)$ What range of addresses can be reached using the MIPS branch if equal $($beq$)$

instruction?

d$)$ How does that change if you decrease the number of registers to $16?$