In the following grammar:

$$\eqalign{ & X:: = X \oplus {Y \over Y} \cr & Y:: = Z*{Y \over Z} \cr & Z:: = id \cr} $$

Which of the following is true?

An $$N$$-bit carry look ahead adder, where $$N$$ is a multiple of $$4,$$ employs $${\rm I}cs$$ $$74181$$ ($$4$$bit $$ALU$$) and $$74182$$ ($$4$$ bit carry look ahead generator). The minimum addition time using the best architecture for this adder is

The correct matching for the following pairs is

Which of the following is essential for converting an infix expression to the postfix form efficiently?