$1$a$.$ Write a function combination which implements the combinatorial function $nCr$ in MIPS assembler.

A straightforward Java implementation without checks is given here:

int combinations$($int $n,$ int $r)\{$

int $c=1$;

for$($int $i=r+1$;$in$;$i++$

$c^{**}=i$;

for$($int $i=1$;$in-r$;$i++$

$\frac{c}{?}=i$;

return $c$;

$\}$

$1$b$.$ The assemble instructions for multiplication and division, respectively, are mul and div.

Use the non$-$recursive factorial example with loops from the class as a starting point.

Write a main function which calls combinations twice with hardcoded $n$ and $r$ as follows:

a$.n=10,r=5($The answer is $252.)$

b$.n=100,r=10($The answer is $17,310,309,456,440$ which takes more than $32$ bits to represent!$)$

Exit your program with the proper syscall.

$1$c$.$ Test and run your program. Provide a screenshot of test runs for the two cases.

$($I haven't learned mflo or mfhi.$)$

$.$text

main:

$\frac{?}{?}$#Call combinations with $n=10,r=5$

$li$ $$a0,10$

$li$ $$a1,5$

jal combinations

# Display result for $n=10,r=5$

$\frac{?}{?}$# Display result

$lw$ ste, svil

$li$ $$ve,1$

move $$ve,1$

sae, ste

syscall

ji jal combinations

# Display result for $n=100,r=10$

iw ste, sv$1$ li sve, $1$

move $$su0,1$ mto

syscall

exit: $l{i}_{\text{s}\text{y}\text{s}\text{c}\text{a}\text{l}\text{l}}$ $v$,10,"$ exit with syscall $10$

# subroutine FACTORIAL$(n)$

# calculates $n**(n-1)**(n-2)**dots**1$ IN: $$a=n$

# OUT:

$$a=n$ $$v0=$ FACTORIAL $(n)$

$$te,$$$t1,$$$ve$

combinations:

#Function proglogue

sw swa, o$($ $$sp$

$$sa,0($$$sp)$ $$s0,4($$$sp)$

$$s1,8($$$sp)$

# Initialize result to $1$

$list0,1$

$sw$ $$t0,$ $$v1$

Error line $10$ column $9$: $"$lw$"$: Too few or incorrectly formatted operands. Expected: lw $t$1,-100($$t$2)$

Error line $21$ column $9$: $"$lw$"$: Too few or incorrectly formatted operands. Expected: lw $t$1,-100($$t$2)$

Error line $42$ column $9$: $"$sw$"$: Too few or incorrectly formatted operands. Expected: sw $t$1,-100($$t$2)$

Error line $52$ column $11$: $"$lw$"$: Too few or incorrectly formatted operands. Expected: lw $$t1,-100($$$t2)$

Error line $54$ column $11$: $"$sw$"$: Too few or incorrectly formatted operands. Expected: sw $t$1,-100($$t$2)$

Error line $64$ column $11$: $"$lw$"$: Too few or incorrectly formatted operands. Expected: lw $$t1,-100($$$t2)$

Error line $66$ column $11$: $"$sw$"$: Too few or incorrectly formatted operands. Expected: sw $t$1,-100($$t$2)$

Assemble: operation completed with errors.