Problem $1$: Write a function add$64$ that adds two input unsigned $64$ bit integers x and y and returns the unsigned $64$ bit integer sum z$,$ i$.$e$.$ z $=$ x $+$ y$.$ In your main function, you should assume that x$,$ y$,$ and z will be stored in the following $6$ registers as follows:

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x: upper $32$ bits in $t$1$ lower $32$ bits in $t$0$

y: upper $32$ bits in $t$3$ lower $32$ bits in $t$2$

z: upper $32$ bits in $t$5$ lower $32$ bits in $t$4$

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Your main function call should read the values of x and y into the stack, invoke add$64,$ and then return z on the stack.

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Also, your function should generate an error only if there is an overflow in the overall $64$ bit addition $($and not if there is an overflow in the addition of the lower $32$ bit components$).$

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Problem $2$:

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Consider the following loop that takes calculates the sum of two arrays:

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$.$data

arr$1$: $.$word $12345678910111213141516$

arr$2$: $.$word $12345678910111213141516$

arr$\_$sum: $.$space $64$ # equal to $16$ words

$.$text

la $a$0,$ arr$1$

la $a$1,$ arr$2$

la $a$2,$ arr$\_$sum

li $s$0,16$ # loop counter$$

loop:$$

beqz $t$0,$ done$$

lw $t$0,$ arr$1$

lw $t$1,$ arr$2$

add $t$2,$ $t$0,$ $t$1$

sw $t$2,$ arr$\_$sum$$

addi $s$0,$ $s$0,-1$

addi $a$0,$ $a$0,4$

addi $a$1,$ $a$1,4$

addi $a$2,$ $a$2,4$

b loop

done:

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A$.$ Calculate the total number of clock cycles needed to run this program if the CPU does not use any pipelines. For simplicity, you may assume that each instruction in the above program is atomic and not a macro that can expand into multiple instructions $($such as li and la$).$ What is the CPI?

B$.$ Calculate the total number of clock cycles needed to run this program if the CPU uses pipelining and automatically inserts nop instructions where needed to avoid data hazards. You may also assume perfect branch prediction, i$.$e$.,$ there are no wasted clock cycles due to control hazards $($so you don't have to insert nop instructions due to beqz instruction$).$