C - Precedence and Associativity

In this tutorial we will learn about precedence and associativity in C programming language.

We evaluate expression based on the rules of precedence and associativity.

Precedence rules

Precedence rules decides the order in which different operators are applied.

Associativity rules

Associativity rules decides the order in which multiple occurences of the same level operator are applied.

Precedence and Associativity table is at the end of this tutorial.

Lets talk about the precedence of the arithmetic operators namely addition, subtraction, multiplication, division and modulus.

High priority is given to multiplication, division and modulus whereas, addition and subtraction gets the low priority.

High * / %
Low  + -

Evaluate the Expressions

In the following example we are given an arithmetic expression consisting of all the 5 operators namely addition, subtraction, multiplication, division and modulus.

We will solve the expression by first targeting high priority operators and then target the low priority operators.

Note! Arithmetic expressions are evaluated from left-to-right.

x = a2 - 3b + a / b

where, a = 4 and b = 2

First we will express the above formula using the arithmetic operators we use in C.

x = a * a - 3 * b + a / b

Now we will replace a and b with their respective values.

x = 4 * 4 - 3 * 2 + 4 / 2

Now we will solve the expression from left to right.

//find x
x = 4 * 4 - 3 * 2 + 4 / 2
  = (4 * 4) - 3 * 2 + 4 / 2      [* high priority operator]
  = 16 - 3 * 2 + 4 / 2
  = 16 - (3 * 2) + 4 / 2         [* high priority operator]
  = 16 - 6 + 4 / 2
  = 16 - 6 + (4 / 2)             [/ high priority operator]
  = 16 - 6 + 2
  = (16 - 6) + 2                 [- low priority operator]
  = 10 + 2
  = (10 + 2)                     [+ low priority operator]
  = 12

So, the final answer of the given expression is 12.

Lets write a C program for the above expression.

#include <stdio.h>
int main(void)
{
  //variables
  int x, a, b;
  
  //initialise
  a = 4;
  b = 2;
  
  //compute x
  x = a * a - 3 * b + a / b;
  
  //output
  printf("x = %d\n", x);
  
  printf("End of code\n");
  return 0;
}

Output

x = 12
End of code

Rules to evaluate given expressions

• Expressions inside the ( ) parenthesis are evalutated first as they assume the highest priority.
• In case of nested parenthesis, evaluate the innermost sub expression.
• Operator with higher precedence gets higher priority.
• If multiple operators are having same precedence then we apply associativity to determine which operator will be evaluated first.

Precedence and Associativity table