You are to write a complete program in MIPS assembly language that evaluates arithmetic expressions. The expressions must be fully parenthesized and include the following expressions
1. + (addition)
2. - (subtraction)
For simplicity all numbers in the expression will have only one base ten digit (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) in them. Your program must be composed of four states: input, convert-to-postfix, evaluate, and output states. At input data must be provided through the console and stored as an array of characters. After one expression is entered your program moves to the convert-to-postfix state. At this state your expression must be converted to the postfix notation using a stack-based algorithm. Your program must then move to the evaluate state which evaluates the postfix expression using a stack-based algorithm. At the output state your code must display the complete expression in the postfix notation followed by the = symbol and the expression's numeric result.
Some valid expressions and their corresponding postfix notations are:
a) ((1-3)+5) corresponds to 13-5+ in postfix notation
b) (1-(3+5)) corresponds to 135+- in postfix notation
Shown below is the Console display for expression a) above:
Console
Expression to be evaluated:
((1 - 3) + 5)
13-5+ = 3
Postfix Notation
Consider a set of all valid, completely parenthesized, infix arithmetic expressions consisting of nonnegative integer digits, and the two operations +, -. The following definition gives all such valid expressions:
1. Any nonnegative integer is a valid infix expression.
2. If a and b are valid infix expressions, then (a+b), and (a-b) are valid infix expressions.
3. The only valid infix expressions are those defined by steps 1 and 2.
The character string ((5-1) +3) is an example of a complete parenthesized expression. All valid fully parenthesized infix expressions will have at least one operator.