Chapter 2, Problem 16E

Explanation of Solution

Grammar for arithmetic expressions in C shown in Figure 6.1:

$\begin{array}{c}\text{expression }\to \text{assignment\_expression}\\ \to \text{ expression , assignment\_expression}\\ \text{assignment\_operator}\to \text{= |*= | /= | \%= | += | -= | <<= | >>= | \&= | ^= | !=}\\ \text{assignment\_expression }\to \text{ conditional\_expression}\end{array}$

$\begin{array}{c}\to \text{ unary\_expression assignment\_operator assignment\_expression}\\ \text{conditional\_expression }\to \text{ logical\_OR\_expression}\\ \to \text{ logical\_OR\_expression ? expression : conditional\_expression}\end{array}$

$\begin{array}{c}\text{logical\_OR\_expression }\to \text{ logical\_AND\_expression}\\ \to \text{logical\_OR\_expression || logical\_AND\_expression}\\ \text{logical\_AND\_expression }\to \text{ inclusive\_OR\_expression}\\ \to \text{ logical\_AND\_expression \&\& inclusive\_OR\_expression}\end{array}$

$\begin{array}{c}\text{inclusive\_OR\_expression }\to \text{ exclusive\_OR\_expression}\\ \to \text{ inclusive\_OR\_expression | exclusive\_OR\_expression}\\ \text{exclusive\_OR\_expression }\to \text{ AND\_expression}\\ \to \text{exclusive\_OR\_expression ^ AND\_expression}\end{array}$

$\begin{array}{c}\text{AND\_expression }\to \text{ equality\_expression}\\ \to \text{AND\_expression \& equality\_expression}\\ \text{equality\_expression }\to \text{ relational\_expression}\\ \to \text{ equality\_expression == relational\_expression}\\ \to \text{ equality\_expression != relational\_expression}\end{array}$

$\begin{array}{c}\text{relational\_expression }\to \text{ shift\_expression}\\ \to \text{ relational\_expression < shift\_expression}\\ \to \text{relational\_expression > shift\_expression}\\ \to \text{ relational\_expression <= shift\_expression}\\ \to \text{ relational\_expression >= shift\_expression}\end{array}$

$\begin{array}{c}\text{shift\_expression }\to \text{ additive\_expression}\\ \to \text{shift\_expression << additive\_expression}\\ \to \text{ shift\_expression >> additive\_expression}\end{array}$

$\begin{array}{c}\text{additive\_expression }\to \text{ multiplicative\_expression}\\ \to \text{ additive\_expression +�}\end{array}$