Expression evaluation, operator precedence, associativity

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Expression: -

  • An expression is a sequence of one or more operands (like variables, constants, and function calls) and operators that the compiler evaluates to produce a single value.

             Examples of Expressions in C:

                 Constant expression                    :                             45

                 Variable expression                     :                             x

                Arithmetic expression                 :                             a + b * c

                Assignment expression               :                             x = 10

                Logical expression                        :                             (x > 5) && (y < 10)

                Complex expression                     :                             (a = b + 5) * (c = d - 3)

                Function call expression             :                             printf("Hello")


Arithmetic Expressions: -

  • An arithmetic expression is a sequence of numeric operands and arithmetic operators that the compiler evaluates to produce a single numerical value.
  • It performs mathematical calculations.
  • The arithmetic operators are addition (+), subtraction (-), multiplication (*), division (/) and modulus (%).
  • Arithmetic expressions follow operator precedence and associativity rules.
  • We can use parentheses ( ) to override default precedence.

 

    Note:

  • The % operator works only with integer operands.
  • / Performs integer division if both operands are integers; otherwise, it performs floating-point division.

         Example: - 


            Output: -


Expression evaluation: -

  • Expression evaluation is the process of executing an expression step by step according to the rules of operator precedence and associativity to obtain a final single value.
  • Every expression in C is evaluated by:

    1. Operands (constants, variables, function results).
    2. Operators (+, -, *, /, %, etc.).
    3. Rules of precedence & associativity.

 

Rules for Evaluation:

  • Parentheses have the highest priority → expressions inside ( ) are evaluated first.
  • Unary operators (++, --, !, etc.) are evaluated next.
  • Multiplication, Division, Modulus (*, /, %) are evaluated before Addition/Subtraction.
  • Addition, Subtraction (+, -) are next.
  • Relational and logical operators come after arithmetic.
  • Assignment (=) is done last.

            Example: -


            Output: -


Operator precedence: -

  • Operator precedence is a set of rules that determines the priority order in which different operators in an expression are evaluated.
  • Operators with higher precedence are evaluated before those with lower precedence.
  • If two operators have the same precedence, then their associativity (left-to-right or right-to-left) decides the order of evaluation.



Associativity: -

  • Associativity is a rule that determines the order or direction of evaluation in which operators of the same precedence are evaluated in an expression.
  • It acts as the "tie-breaker" when precedence alone isn't enough.
  • There are two types of associativity:

 

            1) Left-to-Right: Evaluation proceeds from the leftmost operation to the right.

    • Most operators (like +, -, *, /, %, relational, logical) are evaluated from left to right.

                Example: -


                Output: -


                2) Right-to-Left: Evaluation proceeds from the rightmost operation to the left.

    • Some operators (like assignment =, compound assignment +=, -=, and unary operators ++, --, !) are evaluated from right to left.

                    Example: -


                    Output: -



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