(a+b)*(c+d) Infix To Prefix

3 min read Jun 16, 2024

Converting (a+b)*(c+d) from Infix to Prefix Notation

Infix notation is the standard way we write mathematical expressions, where operators appear between their operands. However, prefix notation, also known as Polish notation, places operators before their operands. This can be useful in computer science for parsing and evaluating expressions.

Let's convert the infix expression (a+b)*(c+d) to prefix notation using the following steps:

1. Identify the operators and operands:

Operators: +, *
Operands: a, b, c, d

2. Prioritize operations:

We need to account for operator precedence. In this case, the multiplication (*) has higher precedence than addition (+). We can use parentheses to clearly indicate the order of operations.

3. Convert each sub-expression:

(a+b): This is a simple addition. To convert to prefix, the operator goes first, followed by the operands. This becomes: +ab
(c+d): Similarly, this converts to: +cd

4. Combine the sub-expressions:

Now we have two prefix sub-expressions: +ab and +cd. Since multiplication has higher precedence, the operator (*) goes first, followed by the two sub-expressions. This gives us the final prefix notation:

*+ab+cd

Example:

To understand this better, let's consider evaluating both expressions:

Infix: (a+b)*(c+d)

Assume a = 2, b = 3, c = 4, d = 5.
(2+3)*(4+5) = 5 * 9 = 45

Prefix: *+ab+cd

Substitute the values: *+23+45
First, evaluate +23: 5
Next, evaluate +45: 9
Finally, evaluate *59: 45

As you can see, both expressions result in the same answer, demonstrating the equivalence of infix and prefix notation.