Let $$ \oplus $$ and $$ \odot $$ denote the Exclusive OR and Exclusive NOR operations, respectively.

Which one of the following is NOT CORRECT?

Consider a carry lookahead adder for adding two $$n$$-bit integers, built using gates of fan-in at most two. The time to perform addition using this adder is

The total number of prime implicants of the function
$$f\left( {w,x,y,z} \right) = \sum {\left( {0,2,4,5,6,10} \right)} $$ _________________.

Given the function $$F = P′ + QR,$$ where $$F$$ is a function in three Boolean variables $$P,Q$$ and $$R$$ and $$P'=!P,$$ consider the following statements.

$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {S1} \right)\,\,\,\,F = \sum {\left( {4,5,6} \right)} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {S2} \right)\,\,\,\,F = \sum {\left( {0,1,2,3,7} \right)} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {S3} \right)\,\,\,\,F = \sum {\Pi \left( {4,5,6} \right)} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {S4} \right)\,\,\,\,F = \sum {\Pi \left( {0,1,2,3,7} \right)} \cr} $$

Which of the following is true?