Expressions

The quadratic equation ax<sup>2</sup> + bx + c = 0.

To perform calculations, you write expressions to calculate the answer in a form similar to that used in mathematics. Consider the quadratic equation:

The quadratic formula.

This equation has two solutions given by the quadratic formula:

To solve this in C++, you write an expression which uses + in place of the ± symbol, to calculate one of the roots, like this: 

(-b + sqrt(b * b - 4 * a * c)) / (2 * a)

An Expression Vocabulary

An expression is any combination of operators and operands which, when evaluated, yields a value.

  1. An operand indicates a value. Operands include:
    • Literals: which represent a value
    • Variables: a storage location containing a value
    • Function calls: which can produce a value
    • Sub-expressions: which yield a value
  2. An operator is a symbol which performs an operation on one or more operands and, subsequently, produces a value. Operators have three characteristics:
    • Arity: the number of operands required. Unary operators require a single operand, while binary operators require two.
    • Precedence: determines which operands "bind to" the operator. Those with higher precedence "stick to" their adjacent operands more closely.
    • Associativity: determines whether operations, at the same level of precedence, should proceed from right-to-left, (called right-associative), or from left-to-right, (called left-associative).

This linked table shows the precedence and associativity for all of the C++ operators.