Assume that on the multi$-$cycle data path all instructions listed below, except for the lw instruction, require $4$ cycles to execute. The lw instruction takes $5$ cycles on the multi$-$cycle data path. Consider the following instruction sequence:

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$$ lui$$ $$2,0$x$4004$

$$ ori$$ $$5,$ $$0,50$

$$ lui$$ $$3,0$x$400$C

$$ lw$$ $$4,80($$$2)$

$$ addu$$ $$6,$ $$5,$ $$5$

$$ lw$$ $$7,0($$$3)$

addiu$$ $$3,$ $$3,4$

$$ addu$$ $$9,$ $$4,$ $$5$

$$ nop

$$ sw$$ $$7,0($$$2)$

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a$)(3)$ How many nano$-$seconds will this instruction sequence take to execute on the multi$-$cycle data path if the clock cycle time is $4$ nano$-$seconds?

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b$)(5)$ How many nano$-$seconds will this instruction sequence take to execute on our $5-$stage MIPS pipelined system if the clock cycle time is $4$ nano$-$seconds?$$ Assume that the pipelined system includes a data hazard unit as well as a data forwarding unit.