We have written binary operations in infix notation, where

Chapter 4, Problem 45

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We have written binary operations in infix notation, where the operation symbol appears between the two operands, as in A + B. Evaluation of a complicated arithmetic expression is more efficient when the operations are written in postfix notation, where the operation symbol appears after the two operands, as in AB+. Many compilers change expressions in a computer program from infix to postfix form. One way to produce an equivalent postfix expression from an infix expression is to write the infix expression with a full set of parentheses, move each operator to replace its corresponding right parenthesis, and then eliminate all left parentheses. (Parentheses are not required in postfix notation.) Thus, A * B + C becomes, when fully parenthesized, ((A * B) + C ) and the postfix notation is AB * C+. Rewrite each of the following expressions in postfix notation: a. (A + B) * (C D) b. A ** B C * D (**denotes exponentiation) c. A * C + B/(C + D * B)