Problem $2(8$ marks$)$

a$)(4$ marks$).$ Suppose $A=D6$ and $B=7C($both in hexadecimal$).$ Show the step by step result multiplying A and $B,$ using the multiplier hardware shown first in Fig. $1$ and then in Fig$\mathrm{.}2.$ Assume A and B are $8-$bit unsigned numbers, stored in hexadecimal format.

b$)(2$ marks$).$ What is the RISC$-$V instruction that gives the lower $32$ bits of the above multiplication of signed integers? Name one register where you will be placing the result and fill in all $32$ bit positions for this instruction $($write it both in assembly and in machine language$).$

c$)(2$ marks$).$ Suppose for an $8-$bit number, each step of operation $($addition or shift$)$ takes $2$ ns$.$ Calculate the time necessary to perform a multiply using the approach given in Fig. $1$ and Fig. $2$ Assume the registers have been initialized. In hardware, shifts of multiplicand and multiplier can be done simultaneously.

Fig. $1$: HW of First $($na$$ve$)$ Multiplication Algorithm

Fig. $2$: Refined HW of Multiplication Algorithm

Solution: