Postfix Notation for Expressions

Infix notation Write the operator between the operands	Postfix notation Write the operator after the operands
3 + 4	3 4 +
3 / 2	3 2 /
2 * ( 3 + 4 )	2 3 4 + * The + operator follows its operands 3 and 4 The * operator follows its operands 2 and (3 4 +)

• Brackets ( ) are not needed in postfix

E.g. ( 2 ( 3 4 + ) * ) is equivalent to 2 3 4 + *

• The operands in a postfix expression are in the same order as in the equivalent infix expression

Write the infix expression A + B / C - 3 in postfix:

A + B / C - 3

A + B C / - 3

A B C / + - 3

A B C / + 3 -

Evaluate the postfix expression 9 3 2 + 8 4 / + -:

9 3 2 + 8 4 / + -

9 5 8 4 / + -

9 5 2 + -

9 7 -

2

Write the postfix expression A 7 D + * in infix:

A 7 D + *

A ( 7 + D ) *

( A * ( 7 + D ) )

Exercises

Write the following infix expressions in postfix:

1. A - 2 + B

2. ( A + 7 ) * ( B - 2 )

3. C + 7 * B

Evaluate the following postfix expressions:

4. 3 2 * 6 2 / +

5. 5 2 7 + 2 1 - + /

Write the following postfix expressions in infix:

6. E F 7 - -

7. G H 2 * A / + 4 -