Assignment Instructions:

1) The Factorial

The factorial of a non-negative integer ??, denoted by ??!, isthe product of all positive integers less than or equal to ??. Thetextbook has an example of a recursive MIPS implementation offactorial. Additionally, a simplified version of the MIPS assemblylanguage recursive implementation of the factorial function isattached. Trace the factorial example carefully using QTSPIM

2) Recursive definition of multiplication

The function ??????????(??, ??) for two positive integers 1 ???, and 1 ? ??, is defined as the following:

??????????(??, 1) = ??; ??????????(??, ??) = ?? + ??????????(??,?? ? 1)

Write a recursive version of ??????????() in C or C++ and apseudo C program (based on chapter 2 in the book) then use theseprograms to develop a MIPS program that gets as input two integers0 < ?? ? 255, and 0 < ?? ? 255, and returns the result of??????????(??, ??) in $v1.

Your deliverable should be the pseudo C and the assembly levelfunction

Given code file one:

//copyable code

1.

.data

messagestr: .asciiz \"Enter Number: \"

.text

.globl main

main:

la $a0, messagestr

#load the data

li $v0, 4

#system call

syscall

#load the data

li $v0, 5

#system call

syscall

#move the data

move $a0,$v0   

jal factorial

move $a0,$v0   

li $v0,1   

syscall

li $v0,10

syscall

factorial:

#add the value

addi $sp,$sp,-8

#store the value  

sw $s0,0($sp)

#store the value   

sw $ra,4($sp)

#move the data

move $s0,$a0

#load the data   

li $v0,0x00000001 # 1

beq $s0,$v0,loop2

#branch instruction  

addi $a0,$s0,-1   

jal factorial

#multiply the data

mult $v0,$s0   

mflo $v0   

j loop3

#loop

loop2:

li $v0,0x00000001

loop3:

lw $ra,4($sp)   

lw $s0,0($sp)   

addi $sp,$sp,8   

jr $ra # return

Given code file two:

######################################################################################    Functional Description: Main program to test Factorial function#    Enter a negative number to terminate run#####################################################################################        .data        .align     2        .textmain:      addiu      $sp, $sp, -8 # Allocate spacemloop:        li       $v0, 4     # Get value for N        sw       $v0, 0 ($sp)        jal       Fac       # Call factorial        or       $v1, $v0, $0        addiu      $sp, 8     # Deallocate space        li       $v0, 10        syscall###################################################################################### Functional Description: Recursive Factorial Fac (N: in, N! :out)#####################################################################################Fac:    lw       $a0,  0 ($sp)    addiu      $sp,  $sp,  -16    #  Allocate      sw       $ra,  12 ($sp)     #  Save return address    sw       $a0,  8($sp)    slti      $t0,  $a0, 2     #  If N is 1 or 0, then return the value 1    beqz      $t0,  Go    li       $v0,  1    b        facretGo:    addi      $a0,  $a0,  -1        #    sw       $a0,  0 ($sp)     #  Pass N-1 to factorial function    jal       Fac           #  Recursive call    lw       $v0,  4($sp)      #  Get (N-1) ! back.    lw       $ra, 12 ($sp)    lw       $a0, 8 ($sp)    mult      $v0, $a0            # N* (N-1) !    mflo      $v0facret:    addiu      $sp, $sp, 16     # Deallocate    sw       $v0, 4 ($sp)    jr       $ra