Assume the following rules of associativity and precedence for expressions: Prec

Question

Assume the following rules of associativity and precedence for expressions:

Precedence

Highest

*, /, not

+, , &, mod

(unary)

=, /=, < , <=, >=, >

and

or, xor

Lowest

Associativity Left to right

Show the order of evaluation of the following expressions by parenthesizing all subexpressions and placing

a superscript on the right parenthesis to indicate order. For example, for the expression a + b * c + d

the order of evaluation would be represented as

((a + (b * c)1 )2 + d)3

a. a * b - 1 + c

b. a * (b - 1) / c mod d

c. (a - b) / c & (d * e / a - 3)

d. -a or c = d and e

e. a > b xor c or d <= 17

f. -a + b

Explanation / Answer

Associativity and precedence of operators :

Precedence

Highest

*, /, not

+, , &, mod

(unary)

=, /=, < , <=, >=, >

and

or, xor

Lowest

Associativity Left to right

a) a*b -1 +c

* has higher precedence than - and +

Associativity is from left to right

Therefore, after parenthesizing expression becomes :

( ( ( a*b )1-1 )2 + c )3

b) a*(b-1)/c mod d

* and / has same precendence but associativity is from left to right

mod has lower precedence than * , /

After parenthesizing expression becomes :

( ( (a* (b-1)1 )2 / c)3 mod d)4

c) (a-b) / c & (d * e / a - 3 )

Precedence of operators is *,/ then - , &

After parenthesizing expression becomes :

( ( (a-b)1 / c)2 & ( ( (d * e)3 / a)4 - 3 )5)6

d)   -a or c = d and e

unary operator has higher precedence than = and then comes 'and' and finally 'or'

After parenthesizing expression becomes :

( (-a)1 or ( ( c = d )2 and e )3)4

e) a > b xor c or d <= 17

After parenthesizing expression becomes :

( ( ( a > b )1 xor c)3 or ( d <= 17 )2 )4

f) -a + b

After parenthesizing expression becomes :

( - ( a + b )1 ) 2

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