Step 1: Explanation of Parallel Adders.
In a parallel adder, each bit of the numbers to be added is processed simultaneously. The carry-out from each full-adder is passed to the next stage as the carry-in for the next full-adder.
Step 2: Analysis of options.
- (A) Parallel carry adder: This is incorrect because a parallel carry adder works without passing carry-out between adders; it is a simpler model.
- (B) Ripple carry adder: This is correct because the carry bit propagates (or "ripples") from one adder to the next, making it slower. Each carry-out becomes the carry-in for the next stage.
- (C) Look-ahead-carry adder: This is incorrect as the look-ahead-carry adder attempts to solve the ripple effect by calculating carry-out bits in advance, improving speed.
- (D) Serial carry adder: This is incorrect because serial adders process one bit at a time, without parallel operation.
Step 3: Conclusion.
The correct answer is (B) Ripple carry adder, as it best matches the description of passing the carry-out to the next adder.
Find the least upper bound and greatest lower bound of \( S = \{X, Y, Z\} \) if they exist, of the poset whose Hasse diagram is shown below:
Suppose \( D_1 = (S_1, \Sigma, q_1, F_1, \delta_1) \) and \( D_2 = (S_2, \Sigma, q_2, F_2, \delta_2) \) are finite automata accepting languages \( L_1 \) and \( L_2 \), respectively. Then, which of the following languages will also be accepted by the finite automata:
(A) \( L_1 \cup L_2 \)
(B) \( L_1 \cap L_2 \)
(C) \( L_1 - L_2 \)
(D) \( L_2 - L_1 \)
Choose the correct answer from the options given below: