Hierarchy of Operations

operators, we may have some problems as to how exactly does it get executed. For example, does the expression 2 * x - 3 * y correspond to (2x)-(3y) or to 2(x-3y)? Similarly, does A / B * C correspond to A / (B * C) or to (A / B) * C? To answer these questions satisfactorily one has to understand the ‘hierarchy’ of operations. The priority or precedence in which the operations inan arithmetic statement are performed is called the hierarchy of operations. The hierarchy of commonly used operators is shown in Figure 1.8.

Now a few tips about usage of operators in general.

(a) Within parentheses the same hierarchy as mentioned in Figure 1.11 is operative. Also, if there are more than one set of parentheses, the operations within the innermost parentheses would be performed first, followed by the operations within the second innermost pair and so on.

(b) We must always remember to use pairs of parentheses. A careless imbalance of the right and left parentheses is a common error. Best way to avoid this error is to type ( ) and then type an expression inside it.
A few examples would clarify the issue further.

Example 1.1: Determine the hierarchy of operations and evaluate the following expression:
i = 2 * 3 / 4 + 4 / 4 + 8 - 2 + 5 / 8
Stepwise evaluation of this expression is shown below:
i = 2 * 3 / 4 + 4 / 4 + 8 - 2 + 5 / 8

i = 6 / 4 + 4 / 4 + 8 - 2 + 5 / 8 operation: *
i = 1 + 4 / 4 + 8 - 2 + 5 / 8 operation: /
i = 1 + 1+ 8 - 2 + 5 / 8 operation: /
i = 1 + 1 + 8 - 2 + 0 operation: /
i = 2 + 8 - 2 + 0 operation: +
i = 10 - 2 + 0 operation: +
i = 8 + 0 operation : -
i = 8 operation: +
Note that 6 / 4 gives 1 and not 1.5. This so happens because 6 and 4 both are integers and therefore would evaluate to only an integer constant. Similarly 5 / 8 evaluates to zero, since 5 and 8 are integer constants and hence must return an integer value.

Example 1.2: Determine the hierarchy of operations and evaluate the following expression:

kk = 3 / 2 * 4 + 3 / 8 + 3
Stepwise evaluation of this expression is shown below:
kk = 3 / 2 * 4 + 3 / 8 + 3
kk = 1 * 4 + 3 / 8 + 3 operation: /
kk = 4 + 3 / 8 + 3 operation: *
kk = 4 + 0 + 3 operation: /
kk = 4 + 3 operation: +
kk = 7 operation: +

Note that 3 / 8 gives zero, again for the same reason mentioned in the previous example.

All operators in C are ranked according to their precedence. And mind you there are as many as 45 odd operators in C, and these can affect the evaluation of an expression in subtle and unexpected ways if we aren't careful. Unfortunately, there are no simple rules that one can follow, such as “BODMAS” that tells algebra students in which order does an expression evaluate. We have notencountered many out of these 45 operators, so we won’t pursue the subject of precedence any further here. However, it can be realized at this stage that it would be almost impossible to remember the precedence of all these operators. So a full-fledged list of all operators and their precedence is given in Appendix A. This may sound daunting, but when its contents are absorbed in small bites, it becomes more palatable.

So far we have seen how the computer evaluates an arithmetic statement written in C. But our knowledge would be incomplete unless we know how to convert a general arithmetic statement to a C statement. C can handle any complex expression with ease. Some of the examples of C expressions are shown in Figure 1.9.