Operator Precedence 
 
 Each of the two grammars below, G1 and G2, defines the syntax of
expressions involving identifier operands and the operators
 
  + 
 Infix Plus 
 
  - 
 Prefix and Infix Minus 
 
  * 
 Multiplication 
 
  / 
 Division 
 
  ** 
 Exponentiation 
 
 These two grammars differ slightly in the order in which operations
are evaluated.
 
   
 Explain the effects of this difference, illustrating your answer by
showing the differences in two parse trees for a particular expression
(one in each grammar; G1 and G2). Provide three such illustrations for
three different sentences defined by the grammars.
 
   
 Which of the two grammars would you select and why? 
 
 Grammar G1 
 
   <e> ::= <e1> | <e> + <e1> | <e> - <e1> 
   <e1> ::= <e2> | <e1> * <e2> | <e1> / <e2>  
   <e2> ::= <id> | - <e2> | <e3> 
   <e3> ::= <id> ** <e2> 
 Grammar G2 
 
   <e> ::= <e1> | <e1> + <e> | <e1> - <e> 
   <e1> ::= <e2> | <e2> * <e1> | <e2> / <e1> 
   <e2> ::= <e2> ** <e3> | <e3> 
   <e3> ::= <id> | - <id> 
 
 Describing BNF using BNF 
 
 Write an BNF grammar to describe STANDARD BNF. Since the symbols you
will be using in the meta-language will be the same as those of the
language being described, you will have to use the technique of
underlining such symbols in the language being described.

Start with: 
 
   <grammar> ::= <production>... 
   <production> ::= <left_side> ::= <right_side> 
   <left_side> ::= <non_terminal> 
    
   <non_terminal> ::= < <character>... > 
   <character> ::= a | b | c | d ... | z

Thanks,

Manohar