$(40$ points$)$ Given the following grammar that accepts a prefix expression,

$S^{\text{'}}E$

$E+EE$

$|E$

$F$

$F$ num $10$

$|$ num $26$

where,$+,$ num $10$ and num $26$ are terminals, num $10$ is a sequence of decimal digits, and num $26$ is a

sequence of lower$-$case English letters. Answer the following questions:

$($a$)(5$ pts$)$ Derive $++512cy$ using right$-$most derivation.

$($b$)(5$ pts$)$ Construct a CFSM for the grammar.

$($c$)(5$ pts$)$ Find the first and follow sets for all non$-$terminals.

$($d$)(5$ pts$)$ Draw the parse table based on your answers in $($b$)$ and $($c$).$

$($e$)(10$ pts$)$ Show the rules$/$actions sections of Flex and Bison specifications for the grammar to

interpret the language where num $10$ is interpreted as a decimal integer and num $26$ as a base$-26$

number. The decimal value of a letter is based on its alphabetic order, $a=0,b=1,$dots, and $z=$

The decimal value of $cy$ can be calculated as $2**26+24=76.$ The unary operator $$ means

negation. As an example, the result of $++512cy$ is $83.$

$($f$)(8$ pts$)$ Based on the grammar and the parse table in $($d$),$ show parse process of the input in

$($a$).$ Annotate each terminal and non$-$terminal on the stack with its attribute value based on your

answer in $($e$).$

$($g$)(2$ pts$)$ How is the parsing process in $($f$)$ related to the derivation in $($a$)?$