Examples of Expressions

We have already seen the precedence of arithmetic operators. We have expressions for different calculations in algebraic form, and in our programs we write them in the form of C statements. Let’s discuss some more examples to get a better understanding.

We know about the quadratic equation in algebra, that is y = ax2 + bx + c. The quadratic equation in C will be written as y = a * x * x + b * x + c. In C, it is not an equation but an assignment statement. We can use parentheses in this statement, this will make the expression statement easy to read and understand. Thus we can rewrite it as y = a * (x * x) + (b * y) + c.

Note that we have no power operator in C, just use * to multiply the same value.

Here is another expression in algebra: x = ax + by + cz2. In C the above expression will be as:

x = a * x + b * y + c * z * z

The * operator will be evaluated before the + operator. We can rewrite the above statement with the use of parentheses. The same expressions can be written as:

x = (a * x) + (b * y) + c * ( z * z)

Lets have an other expression in algebra as x = a(x + b(y + cz2)). The parentheses in this equation forces the order of evaluation. This expression will be written in C as:

x = a * (x + b * (y + c * z * z))

While writing expressions in C we should keep in mind the precedence of the operators and the order of evaluation of the expressions (expressions are evaluated from left to right). Parentheses are used in complicated expressions. In algebra, there may be curly brackets { } and square brackets [ ] in an expression but in C we have only parentheses ( ). Using parentheses, we can make a complex expression easy to read and understand and can force the order of evaluation. We have to be very careful while using parentheses, as parentheses at wrong place can cause an incorrect result. For example a statement x = 2 + 4 * 3 results x = 14. As * operator is of higher precedence, 4 * 3 is evaluated first and then result 12 is added to 4 which gives the result 14. We can rewrite this statement, with the use of parentheses to show it clearly, that multiplication is performed first. Thus we can write it as x = 2 + (4 * 3). But the same statement with different parentheses like x = (2 + 4) * 3 will give the result 18, so we have to be careful while using parenthesis and the evaluation order of the expression.

Similarly the equation (b^2 – 4ac)/2a can be written as ( b * b – 4 * a * c) / ( 2 * a ). The same statement without using parentheses will be as b * b – 4 * a * c / 2 * a. This is wrong as it evaluates to b^2 – 4ac/2a (i.e. 4ac is divided by 2a instead of (b^2-4ac)).

For previous lesson click here: Sample Program
For next lesson click here: Use of Operators

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Examples of Expressions

Precedence of Operators

The arithmetic operators in an expression are evaluated according to their precedence. The precedence means which operator will be evaluated first and which will be evaluated after that and so on. In an expression, the parentheses ( ) are used to force the evaluation order. The operators in the parentheses( ) are evaluated first. If there are nested parentheses then the inner most is evaluated first.

The expressions are always evaluated from left to right. The operators *, / and % have the highest precedence after parentheses. These operators are evaluated before + and – operators. Thus + and – operators has the lowest precedence. It means that if there are * and + operators in an expression then first the * will be evaluated and then its result will be added to other operand. If there are * and / operators in an expression (both have the same precedence) then the operator which occurs first from left will be evaluated first and then the next, except you force any operator to evaluate by putting parentheses around it.

The following table explains the precedence of the arithmetic operators:

Operators	Operations	Precedence (Order of evaluation)
( )	Parentheses	Evaluated first
*, /, or %	Multiplication, Division, Modulus	Evaluated second. If there are several, they are evaluated from left to right
+ or -	Addition, Subtraction	Evaluated last. If there are several, they are evaluated from left to right

Lets look some examples.

What is the result of 10 + 10 * 5 ?

The answer is 60 not 100. As * has higher precedence than + so 10 * 5 is evaluated first and then the answer 50 is added to 10 and we get the result 60. The answer will be 100 if we force the addition operation to be done first by putting 10 + 10 in parentheses. Thus the same expression rewritten as (10 + 10) * 5 will give the result 100. Note that how the parentheses affect the evaluation of an expression.

Similarly the expression 5 * 3 + 6 / 3 gives the answer 17, and not 7. The evaluation of this expression can be clarified by writing it with the use of parentheses as (5 * 3) + (6 / 3) which gives 15 + 2 = 17. Thus you should be careful while writing arithmetic expressions.

Tips

• Use spaces in the coding to make it easy to read and understand
• Reserved words can not be used as variable names
• There is always a main( ) in a C program that is the starting point of execution
• Write one statement per line
• Type parentheses ’( )’ and braces ‘{ }’ in pairs
• Use parentheses for clarification in arithmetic expressions
• Don’t forget semicolon at the end of each statement
• C Language is case sensitive so variable names x and X are two different variables

For previous lesson click here: Arithmetic Operators
For next lesson click here: Sample Program

the easiest way to learn programming
introduction to programming
Precedence of Operators