scanning processsuppose we are evaluating string containing nine non-blank characters and have scanned the first threea ( dat this pointwe have no way of knowing if the addition operation is to be performed on the two variables and or if we have to save this information for later after moving to the the next character ( dwe encounter the division operator and know that the addition is not the first operation to be performed is the division the first operation to be performedit does have higher precedence than the additionbut it may not be the first operation since parentheses can override the order of evaluation we will have to scan more of the string to determine which operation is the first to be performed ( dafter determining the first operation to be performedwe must then decide how to return to those previously skipped this can become tedious process if we have to continuously scanned forward and backward through the string in order to properly evaluate the expression to simplify the evaluation of mathematical expressionwe need an alternative representation for the expression representation in which the order the operators are performed is the order they are specified would allow for single left-to-right scan of the expression string three different notations can be used to represent mathematical expression the most common is the traditional algebraic or infix notation where the operator is specified between the operands + the prefix notation places the operator immediately preceding the two operands +abwhereas in postfix notationthe operator follows the two operands abat first glancethe different notations may seem to be nothing more than different operator placement but the postfix and prefix notations have the advantages that neither uses parentheses to override the order of precedence and both create expressions in unique form in other wordseach expression is unique and produces specific result unlike infix notation in which the same expression can be written in multiple ways converting from infix to postfix infix expressions can be easily converted by hand to postfix notation the expression would be written as ab+cin postfix form the evaluation of this expression would involve first adding and and then subtracting from that result we will examine the evaluation of postfix expressions laterfor now we focus on the conversion from infix to postfix