Question 1: Describe how a linear search algorithm works when searching for a number in a list of unsorted numbers. What are its advantages and disadvantages?

Answer: A linear search checks each element in the list one by one from the start until it finds the target number or reaches the end. Advantages include simplicity and no need for sorting; disadvantages include it being slow for large lists because it may check every item.

Question 2: Explain the difference between linear search and binary search. Under what conditions can binary search be used?

Answer: Linear search checks each element sequentially and works on unsorted lists. Binary search repeatedly divides a sorted list to find the target, making it faster. Binary search can only be used if the list is sorted.

Question 3: List one real-life scenario where binary search could be applied and explain how it would work.

Answer: Searching for a word in a dictionary: open the middle of the dictionary, check if the word is before or after, then continue narrowing down the range until the word is found.

Question 4: Complete the truth table for an AND logic gate with inputs A and B, and output C.

Answer: A B | C 0 0 | 0 0 1 | 0 1 0 | 0 1 1 | 1

Question 5: Complete the truth table for an OR logic gate with inputs A and B, and output C.

Answer: A B | C 0 0 | 0 0 1 | 1 1 0 | 1 1 1 | 1

Question 6: Draw a logic circuit that uses NOT, AND, and OR gates to represent the following expression: NOT(A AND B) OR C.

Answer: A correct sketch would show an AND gate with inputs A and B, the output going into a NOT gate, and then an OR gate that also takes input C. The OR gate’s output is the final result.

Question 7: Sketch a simple circuit diagram for an AND gate. Label all parts clearly.

Answer: A correct sketch would include a rectangle labeled 'AND', two input lines entering the rectangle, and one output line leaving it. All parts should be clearly labelled.

Question 8: Explain how the AND gate works, including what the output will be if both inputs are true, and if either input is false.

Answer: The AND gate outputs true only if both inputs are true. If both are true, output is true. If either input is false, output is false.

Question 9: Describe how a binary search algorithm would behave if the list is not sorted. Why is sorting important before applying binary search?

Answer: Binary search would not work correctly on an unsorted list because it relies on dividing the list in a way that assumes the data is ordered. Sorting ensures the list is in a sequence that binary search can efficiently divide and conquer.

Question 10: Given a list of numbers: 3, 7, 15, 23, 42, explain step-by-step how a binary search would find the number 15.

Answer: First, compare 15 with the middle number, 15 (at index 2). Since it matches, the search stops and returns the position. If not, it would compare with the middle of the relevant half, narrowing down the search.

Question 11: Sketch a truth table for an XOR (exclusive OR) gate with inputs A and B and output C. Label the headers clearly.

Answer: A B | C 0 0 | 0 0 1 | 1 1 0 | 1 1 1 | 0

Question 12: Draw and label a logic circuit that uses an XOR gate to compare two inputs, A and B, and outputs true if exactly one input is true.

Answer: A correct sketch would show an XOR gate with inputs A and B, and the output labeled as the result. The circuit should clearly depict the gate and input lines.