Question

In Assembly Language

Please display results and write assembler code in (gcd.s)

The Euclidean algorithm is a way to find the greatest common divisor of two positive integers, a and b. First let me show the computations for a=210 and b=45.

Divide 210 by 45, and get the result 4 with remainder 30, so 210=4·45+30.

Divide 45 by 30, and get the result 1 with remainder 15, so 45=1·30+15.

Divide 30 by 15, and get the result 2 with remainder 0, so 30=2·15+0.

The greatest common divisor of 210 and 45 is 15.

Formal description of the Euclidean algorithm

Input Two positive integers, a and b.

Output The greatest common divisor, g, of a and b.

Internal computation

1. If a<b, exchange a and b.

2. Divide a by b and get the remainder, r. If r=0, report b as the GCD of a and b.

3. Replace a by b and replace b by r. Return to the previous step.

Your assignment is to write an assembler code (gcd.s) that asks the user two positive numbers and calculates their greatest common denominator.

For example, you program should produce the following outputs:

Enter first positive integer: 6

Enter second positive integer: 8

The GCD is 2

Answer 1

DATA SEGMENT
  NUM1 DW 6
  NUM2 DW 8
  GCD DW ?
DATA ENDS
CODE SEGMENT
  ASSUME CS:CODE,DS:DATA
  START: MOV AX,DATA   ;Load the Data to AX.
         MOV DS,AX     ;Move the Data AX to DS.
         MOV AX,NUM1   ;Move the first number to AX.
         MOV BX,NUM2   ;Move the second number to BX.
  UP: CMP AX,BX        ;Compare the two numbers.
      JE EXIT          ;If equal, go to EXIT label.
      JB EXCG          ;If first number is below than second,
                       ;go to EXCG label.
  UP1: MOV DX,0H       ;Initialize the DX.
       DIV BX          ;Divide the first number by second number.
       CMP DX,0        ;Compare remainder is zero or not.
       JE EXIT         ;If zero, jump to EXIT label.
       MOV AX,DX       ;If non-zero, move remainder to AX.
       JMP UP          ;Jump to UP label.
  EXCG:XCHG AX,BX     ;Exchange the remainder and quotient.
       JMP UP1        ;Jump to UP1.
  EXIT:MOV GCD,BX     ;Store the result in GCD.
       MOV AH,4CH
       INT 21H
  CODE ENDS
  END START