Description
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Write a MIPS program to do the following:
The program should input an integerof at most 4 decimal digits – this is the modulus, n. The program should input a stringof 12 decimaldigits (most significant digit first). This represents a 12-digit integer(padded with 0s, if needed). Call it a.
The program should compute amod nand display this value on the screen (result should be between 0 and n-1, i.e., 0 ≤ a mod n ≤ n-1).
Your program should prompt the user for input as shown below.
Your program should include a couple of subroutines. (Ideally, at least one of them should
be a non-leaf routine.)
Constraints:n>=1, integer represented by a>=0.
Sample run:
Enter modulus:1000
Enter string of 12 decimal digits:123456789012
123456789012 mod 1000 = 12 Wish to continue?:Y
Enter modulus:25
Enter string of 12 decimal digits:246801357988
246801357988 mod 25 = 13 Wish to continue?: N
Output by your program is in blue color.
You may wish to use the following easily provable theorems from Modulo Arithmetic:
(a + b) mod n = ( (a mod n) + (b mod n) ) mod n
and
(a * b) mod n = ( (a mod n) * (b mod n) ) mod n
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Implement a recursive function to compute the gcd of two integers. (The gcd is the greatest common divisor or common factor shared by two integers. For example, gcd(210, 112) = 14.)
For two integers m and n , m >= n , gcd ( m , n ) = n if m % n = 0.
Otherwise, gcd( m , n ) = gcd( n , m % n ).
So, gcd(210,112) = gcd(112,98) = gcd(98,14) = 14.
Your function should prompt the user for the two integer inputs m and n and then print the value of gcd ( m , n ).
Sample run:
Enter m:210
Enter n:112
gcd(210,112) = 14
Wish to continue?:Y
Enterm:462
Entern:363
gcd(462,363) = 33
Wish to continue?:N
Output by your program is in blue color.
