$$A$$ $$4$$-bit carry look ahead adder, which adds two $$4$$-bit numbers, is designed using $$AND,$$ $$OR,$$ $$NOT,$$ $$NAND,$$ $$NOR$$ gates only. Assuming that all the inputs are available in both complemented and uncomplemented forms and the delay of each gate is one time unit, what is the overall propagation delay of the adder? Assume that the carry network has been implemented using two-level $$AND$$-$$OR$$ logic.

What is the result of evaluating the following two expressions using three $$-$$ digit floating point arithmetic with rounding?
$$\eqalign{ & \left( {113. + - 111.} \right) + 7.51 \cr & 113. + \left( { - 111. + 7.51} \right) \cr} $$

Given the following input (4322, 1334, 1471, 9679, 1989, 6171, 6173, 4199) and the hash function x mod 10, which of the following statements are true?
i) 9679, 1989, 4199 hash to the same value
ii) 1471, 6171 has to the same value
iii) All elements hash to the same value
iv) Each element hashes to a different value

In a depth-first traversal of a graph G with n vertices,k edges are marked as tree edges. The number of connected components in G is