$(10$ pts$)$ Consider an ISA made up of only the following $12$ similar$-$to$-$LEGv$8$ instructions.

$\backslash$table$[[$ADD R$1,$ R$2,$ R$3,//$ add contents of R$3$ to R$2$ and put in R$1],[$SUB R$1,$ R$2,$ R$3,//$sub contents of R$3$ to R$2$ and put in R$1],[$AND R$1,$ R$2,$ R$3,//$ and contents of R$3$ to R$2$ and put in R$1],[$OR R$1,$ R$2,$ R$3,//$ or contents of R$3$ to R$2$ and put in R$1],[$ADDI R$1,$ R$2,$ #$5,//$ add contents of R$2$ and $5$ and put in R$1],[$ORI R$1,$ R$2,$ #$5,//$ or the contents of R$2$ and $5$ and put in R$1],[$LDUR R$1,[$R$2,$ #$4],//$ load contents of memory addressed by R$2$ and put in R$1],[$STUR R$1,[$R$2,$ #$4],//$ store contents of R$1$ to memory addressed by R$2],[$MUL R$1,$ R$2,$ R$3,//$ multiply contents of R$3$ with R$2$ and put in R$1],[$CBZ R$1,$ label,$//$ if contents of R$1$ does not equal R$2,$ goto label$],[$CBNZ R$2,$ label,$//$ if contents of R$1$ equals R$2,$ goto label$],[$B label,$//$ goto label$]]$

a$)$ How many bits for opcode are needed in order to encode the above instructions?

b$)$ If the ISA has only $7$ general$-$purpose registers $($R$0$ thru R$6)$ and it uses $16$ bits to represent each of the above instructions. It could have several encoding formats. How many bits are needed for each register? What is the largest immediate value that can appear in the instruction? How far can you branch $($i$.$e$.,$ can jump how many instructions$)?$ Why?

c$)$ If all registers are $16-$bit, what is the approximate size of the data memory? Why?