Final answer:
To design a circuit that adds 2 to even numbers and 3 to odd numbers and ensures an even output, utilize digital logic with adders and multiplexers to perform the necessary operations and checks.
Step-by-step explanation:
The student has asked to design a circuit board that can add 2 to even numbers and 3 to odd numbers while ensuring the output is always even. To implement this on a circuit board, one could use a combination of digital logic components such as adders, multiplexers (MUX), and basic logic gates (AND, OR, NOT). The circuit would first determine if the input number is even or odd using a modulo operation (typically, checking the least significant bit). If the input is even, the circuit would use an adder to add 2 to the number. If the input is odd, it would add 3. To ensure the result is always even, if the output after adding is odd (which can only happen when adding 3 to an odd number), the circuit would then add 1 more to make it even.
A possible implementation:
- Use a 2:1 MUX to select between adding 2 or adding 3, with the selection line connected to the least significant bit of the number (0 for even, 1 for odd).
- After the MUX, pass the result to an adder circuit that either outputs the result directly if it's even, or adds 1 if it's odd using another MUX controlled by the least significant bit of the sum.
This approach leverages digital logic to accomplish the numerical operation and conditional logic required for the task, demonstrating a practical application of digital electronics principles.