I have noticed that multiplexers are not included in the list of components we are allowed to use in exercise 9, and just want to make sure it is on purpose, as i haven’t yet found an implementation to the function in Theorem 2 without one.

Multiplexers are indeed not allowed in this exercise. Two reasons why this is not a problem:

- When you have a conditionally defined function where one of the conditional outputs is zero, this can be implemented using only basic logic gates. For example, look at the parity-filter circuit in the last question of Project 0.
- When Logisim’s divider is fed with a divisor equal to zero, it treats it as if the divisor was 1.