Question 1: Convert the hexadecimal number '1A' to its decimal equivalent.

Answer: 26

Question 2: Convert the decimal number 45 into hexadecimal.

Answer: 2D

Question 3: Explain in your own words what a hexadecimal number is and why it is used in computing.

Answer: A hexadecimal number uses base 16, which means it has 16 different symbols (0-9 and A-F). It is used in computing because it can represent binary data more compactly and is easier for humans to read than long strings of binary numbers.

Question 4: Given the hexadecimal number 'FF', what is its value in decimal?

Answer: 255

Question 5: Write the hexadecimal equivalent of the decimal number 100.

Answer: 64

Question 6: Describe how a computer might use hexadecimal numbers to represent colours in digital images.

Answer: Computers use hexadecimal numbers to represent colours because they can easily encode the red, green, and blue (RGB) components of a colour. Each component is represented by two hexadecimal digits, making it simple to specify any colour in the RGB spectrum.

Question 7: Complete the truth table below for the AND logic gate:

Answer: [{"Output":"0","Input A":"0","Input B":"0"},{"Output":"0","Input A":"0","Input B":"1"},{"Output":"0","Input A":"1","Input B":"0"},{"Output":"1","Input A":"1","Input B":"1"}]

Question 8: Draw a logic circuit diagram for an OR gate. Label the inputs and output clearly.

Answer: A correct sketch would include the OR gate symbol with two labeled inputs and one labeled output. The inputs are connected to the gate, and the output is derived from the OR operation.

Question 9: Sketch a design for a simple hexadecimal to binary converter circuit. Use labels to show the main components involved.

Answer: A correct sketch would include an input labeled as hexadecimal, a process or conversion block, and an output showing binary digits. Labels should identify key parts like 'Hexadecimal input', 'Conversion logic', and 'Binary output'.

Question 10: What is the hexadecimal representation of the decimal number 255? Explain how you arrived at your answer.

Answer: FF. Because 255 in decimal is the maximum value for an 8-bit number, and in hexadecimal, it is represented as 'FF', which is (15×16) + 15.

Question 11: Create a short explanation of why hexadecimal numbers are important in computer programming.

Answer: Hexadecimal numbers are important because they provide a compact way to represent binary data, making it easier for programmers to read, write, and debug code related to memory addresses, colour codes, and low-level data.