Problem $1.$ Single$-$cycle Datapath $(20$ points$)$: Modify the single$-$cycle data path given below to support an immediate type instruction called "use constant" $($uc$).$

use constant

$\backslash$table$[[31,2625,2120,1615],[\backslash$table$[[$uc$],[110011]],$rs$,$rt$,$immediate,,,$]]$

Format: uc rs$,$ imm # Memory$[$ GPR$[$ rt$]]=$ GPR$[$ rs$]+2$ immediate

# GPR: general purpose register $($register file$)$

You are allowed to add new datapath component$($s$),$ wire$($s$)$ and$/$or mux$($es$).$ Do not modify the main functional unit themselves $($the memory, register file and ALU$).$ You are not allowed to make a change to the $"$uc$"$ specification. You car assume that any unused field in the instruction is set to $0.$ Try to keep your diagram neat!

Note: While we're primarily concerned about correctness, full points will only be rewarded to most efficient solution $($minimum cycle time and area overhead$)$ for the uc instruction. Assume that the ALU, Memory, and Register file each take $3$ns$,$ and all other datapath components take $1$ns$.$ Each additional input to an existing mux introduces $1$ns delay. Your modification$($s$)$ should not affect the functionally of the other types of instructions.

$3$

$\backslash$table$[[$Opcode$,$PCSrc$,$RegDst,RegWrite,ALUSrc,ALUOp,MemRead,MemWrite,MemToReg$],[$uc$,,,,,,,,]]$