Given two operands and and an operator, the infix notation implies that O will be placed in between a and b i.e. Without the added complication of parentheses and other rules of precedence, computers can evaluate prefix and postfix expressions simply as a set of instructions for them to follow in the order they are given. Prefix and postfix notations, on the other hand, build compound expressions that are never ambiguous, as they only ever yield a singular possible result that depends solely on the order in which the operators and operands appear in an expression when processed in a linear fashion. This doesn’t lend itself to the way computers generally perform operations: sequentially, and one-at-a-time. Infix expressions are, therefore, not evaluated in a linear, left-to-right fashion, but in an order of priority determined by the laws of operator precedence.
Conventions governing operator precedence-which includes the use of parentheses-are a means of removing the very likely possibility that a given combination of operators and operands would otherwise give rise to ambiguous expressions, such as 12 ÷ 6 × 3, which could evaluate to either 6 or ⅔. Humans use infix expressions on a day-to-day basis, but the nature of infix notation means that compound expressions are generally not evaluated in a linear fashion.
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