1. Evaluate a short algebraic expression using code with three-operand instructi

Question

1.
Evaluate a short algebraic expression using code with three-operand instructions. The expression should have a minimum of three operands and 2 operators. Operands may be alpha or numeric. You may only use registers A through F, plus X and T. Registers A through F may not be changed, i.e. their values are fixed. Register T may be used as a temporary register, and Register X must contain the final answer. Show the postfix for the expression, and then use a stack to evaluate the expression.

***It is important to note that operational hierarchy dictates that:
we first perform all arithmetic inside inner parentheses;
then inside outer parentheses;
then do multiplication and division operations before addition and subtraction operations.

******This is an example provided by the teacher, consider X=A +B + C * D
The three-operand instructions would be:
   ADD X, A, B
   MUL T, C, D
   ADD X, X, T
The Postfix would be AB+CD*+
The stack would be:
        PUSH    / A onto the stack
        PUSH    / B onto the stack
        ADD      /pop A & B, add them, and push the answer back on the stack
        PUSH    /C
        PUSH   / D
        MUL   /pop C & D, multiply them, and push the answer back on the stack
        ADD    / pop X & T, add them, and push the answer back on the stack
         POP    / X off the stack**************   end of example provided by teacher

Please don’t use the example above just solve a different algebraic expression.

Explanation / Answer

Conisder this Infix Expression : (A +B * C) / (D + E * F)

NOTE POINTS:

1) Infix Expression Contains Operators between Operands.Example A+B.Here A and B are Operands and + (plus) is Operator.

2)In Postfix Expression Operator is Placed at the end of Operands .Example AB+ (its Infix is A+B).

3)In this example symbol ' * ' referrs to Multiplication Operation.

Three-Operand Instructions for Postfix Expression:

Infix Expression :( A + B * C ) / ( D + E * F)

MUL X,B,C

ADD X,X,A

MUL T,E,F

ADD T,T,D

DIV X,X,T

The Postfix Expression would be : X = A B C * + D E F * + /

NOTE POINT:

consider this code MUL X,B,C   

here X is destination register , the operation is performed like this X <--- B * C , Product of B and C is Stored in X.

Evaluation of Postfix Expression using Stack:

NOTE POINT:

Stack is a Data Structure which follows FIRST IN LAST OUT Policy.Stack contains 2 operations PUSH AND POP.The operation involves insertion of element into the Stack and Pop involves deletion of element from the Stack.

Postfix Expression : X = A B C * + D E F * + /

The Stack would be:

PUSH A

PUSH B

PUSH C

MUL / pop B and C , multiply them, and push the answer back on the stack .

ADD / pop A and also the value which is on the top of the Stack that is Product of B & C add them, and push the answer back on the stack

PUSH D

PUSH E

PUSH F

MUL   / pop E and F , multiply them, and push the answer back on the stack .

ADD /pop D and also the value which is on the top of the Stack that is Product of E & F add them, and push the answer back on the stack

DIV / Division operation

POP / pop the value on the top of the Stack and store in Register X

EXAMPLE :

let Register values as A = 8 , B = 2 , C = 5 , D = 3 , E = 3 , F = 2

Infix Expression : 8+2*5/3+3*2

Postfix Expression :825*+332*+/

After evaluation of the Postfix Expression we got 2 as result which is placed on top of the Stack .

STEPS REMAINING STRING INSTRUCTION STACK 1 8 2 5 * + 3 3 2 * + / PUSH 8 8 2 2 5 * + 3 3 2 * + / PUSH 2 8,2 3 5 * + 3 3 2 * + / PUSH 5 8,2,5 4 *+332*+/ MUL 8,10 5 +332*+/ ADD 18 6 332*+/ PUSH 3 18,3 7 32*+/ PUSH 3 18,3,3 8 2*+/ PUSH 2 18,3,3,2 9 *+/ MUL 18,3,6 10 +/ ADD 18,9 11 / DIV 2

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