abcdef+/-*some computer languages also have an operator for raising quantity to power (typically the character)but we'll ignore that possibility in this discussion besides infix and postfixthere' also prefix notationin which the operator is written before the operands+ab instead of abthis is functionally similar to postfix but seldom used translating infix to postfix the next several pages are devoted to explaining how to translate an expression from infix notation into postfix this is fairly involved algorithmso don' worry if every detail isn' clear at first if you get bogged downyou may want to skip ahead to the section"evaluating postfix expressions in understanding how to create postfix expressionit may be helpful to see how postfix expression is evaluatedfor examplehow the value is extracted from the expression +*which is the postfix equivalent of *( + (notice that in this discussionfor ease of writingwe restrict ourselves to expressions with single-digit numbersalthough these expressions may evaluate to multidigit numbers how humans evaluate infix how do you translate infix to postfixlet' examine slightly easier question firsthow does human evaluate normal infix expressionalthoughas we stated earlierthis is difficult for computerwe humans do it fairly easily because of countless hours in mr klemmer' math class it' not hard for us to find the answer to + + or *( + by analyzing how we do thiswe can achieve some insight into the translation of such expressions into postfix roughly speakingwhen you "solvean arithmetic expressionyou follow rules something like this you read from left to right (at least we'll assume this is true sometimes people skip aheadbut for purposes of this discussionyou should assume you must read methodicallystarting at the left when you've read enough to evaluate two operands and an operatoryou do the calculation and substitute the answer for these two operands and operator (you may also need to solve other pending operations on the leftas we'll see later this process is continued--going from left to right and evaluating when possible-until the end of the expression in tables and we're going to show three examples of how simple infix expressions are evaluated laterin tables and we'll see how closely these evaluations mirror the process of translating infix to postfix to evaluate + - you would carry out the steps shown in table table evaluating + - item read expression parsed so far comments