Is there a limitation on the number of logic gates we can use?
For example if I can build two circuits with the same functionality, one that has an mux
and the other has multiple XOR gates instead, is there a preferred way in which I should build the circuit?
Unless explicitly specified, either of the options are okay. In general, if you want to decide which approach is better, you need to take into account the real-world cost and delay of the gates. For the project, you can assume that all gates have a cost of 1. So in your example, the circuit with one MUX will be better than the circuit with multiple XORs.
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Will the number of gates effect the grade? For instance if I use 5 gates while the minimum possible to complete the exercise is 3.