Question

Sample Execution : ** Recursive Euclidean Algorithm to calculate GCD **

Type a positive integer for A: -2

Sorry, you must enter a positive integer (>0). Please try again.

** Recursive Euclidean Algorithm to calculate GCD **

Type a positive integer for A: 35

Type a positive integer for B: 63

The GCD is 7

Write a MIPS assembly program that prompts the user for 2 positive integers (>0). Then it uses the Recursive Euclidean Algorithm to calculate GCD (the Greatest Common Divisor). Please see below for the Recursive Euclidean Algorithm in Java and C++.

Make sure program the error for negative number.

Sample Execution : ** Recursive Euclidean Algorithm to calculate GCD **

Type a positive integer for A: -2

Sorry, you must enter a positive integer (>0). Please try again.

// Java: Euclidean Algorithm to calculate GCD // import java.util.Scanner; public class FindGCD { public static void main(String[] args) { Scanner input = new Scanner(System.in); System.out.println("The Euclidean Algorithm to calculate GCD.\n"); System.out.println("Enter a positive integer A: "); int A = input.nextInt(); System.out.println("Enter a positive integer B: "); int B = input.nextInt(); if (A < 1 || B < 1) System.out.println("\nError, please enter a positive (>0) integer."); else { if (A < B) { int temp = A; A = B; B = temp; } System.out.println("The GCD is :" + GCD(A, B)); } } public static int GCD(int A, int B) { if (B == 0) return A; else return GCD(B, A % B); } }

// C++: Euclidean Algorithm to calculate GCD // #include using namespace std; int GCD(int A, int B) { if (B == 0) return A; else return GCD(B, A%B); } int main() { int A, B; cout > A; cout > B; if (A < 1 || B < 1) cout 0) integer.\n”; else { if (A < B) { int temp = A; A = B; B = temp; } cout << "The GCD is :" << GCD(A, B) << endl; } return 0; }

Answer 1

.text
         .globl __start

__start: li $v0, 4
         la $a0, First
         syscall                # Ask for the first integer

         li $v0, 5
         syscall                # Read an integer
         add $t0, $0, $v0       # and store it in $t0

         li $v0, 4
         la $a0, Second
         syscall                # Ask for the second integer

         li $v0, 5
         syscall                # Read an integer
         add $t1, $0, $v0       # and store it in $t1

# Include here one of the following two versions

# Version 1: based on integer division

loop:    div $t0, $t1
         mfhi $t2               # $t2 = $t0 mod $t1
         add $t0, $0, $t1       # $t0 = $t1
         add $t1, $0, $t2       # $t1 = $t2
         bne $t1, $0, loop

# Version 2: based on subtract

#loop:    beq $t0, $t1, exit     # if the numbers are equal then exit
#         bgt $t0, $t1, skip     # subtract the smaller from the bigger
#         sub $t1, $t1, $t0      # and replace the bigger with the result
#         b loop                 # then continue
#skip:    sub $t0, $t0, $t1
#         b loop

# end of inclusion

exit:    li $v0, 4
         la $a0, Ans
         syscall                # Print "The GCD is: "

         add $a0, $0, $t0
         li $v0, 1
         syscall                # Print GCD

         li $v0, 4
         la $a0, nl
         syscall                # Print new line

         b __start              # Go to __start (Press Ctrl-C for exit)

         .data
First:   .asciiz "Calculating GCD of two integers.\nEnter first integer: "
Second: .asciiz "Enter second integer: "
Ans:     .asciiz "Their GCD is: "
nl:      .asciiz "\n\n"