What is Postfix Notation

In postfix notation, the operator appears after the operands, i.e., the operator between operands is taken out & is attached after operands.

Example1 − Translate a ∗ d − (b + c) into Postfix form.

Solution

ad ∗ bc + −

Example2 − Convert a + (b ∗? c) is in Postfix form.

Solution

Here ? represents the unary minus operator.

a b c ? ∗ +

Example3 − Convert Postfix Expression into Infix Expression using Stack Implementation

a d ∗ bc + −

Solution

Example4 − Calculate the value for the postfix expression.

57 + 2 ∗ 3/

Solution

This expression can be evaluated by using a stack. Each symbol can be inserted sequence wise & the operator can be applied on operands lying at the top of the stack and next to it.

∴ Answer is 8.

Postfix Notations used in Control Statements

• Jump − Jump to label ? can be written in postfix notations as −

                                         ?jump

• jlt (Jump if less than) − e₁ e₂ ? jlt makes the jump to label if e₁ has a smaller value than e₂.

  
  

• jeqz (jump if equal to zero) − e ? jeqz causes jump to ? if e has the value zero.

  
  

Example5 − Convert the following statement into postfix Notation.

if e then x else y

Solution

If − else statement can be written as

If e then

   x

else

?₁: y

?₂: exit

The postfix Notation will be

Example6 − Convert expression into Postfix Notation.

if a then if c + d then a + c else a * c else a + b.

Solution

It can be written as

if a then

      if c + d then

            a + c

           else

                a * c

      ?₁:

      else

      ?₂: a + b

      ?₃: exit