Electrical – Implementing 3 variable boolean function using mux 4 to 1 and inverter

How well a karnaugh map can simplify is downto the creator of the map with regards to drawing optimal loops.

How to determine whether what has been drawn (post further boolean reduction) is not really possible with k-maps on their own

One option is the use of Espresso Heuristic Logic reduction via a fantastic piece of software called: Logic friday ( http://www.sontrak.com/ ) Quite often this has reduced some logic of mine even further as I usually forget the odd one or two don't care states

The real question however is ... is this check on reduction for personal/professional use (in which case carry on) or homework? because if it is homework and logicFriday realises a further simplification, you had better be able to realise it via k-maps for the marks

The less efficient (and maybe more obvious) way is to connect fixed logic levels to each input of the multiplexer. You need a 2^N input multiplexer for N inputs. So, an 16-input mux for any function of 4 bits.

If, instead, you connect the respective inputs to either one of the inputs (that doesn't go to the multiplexer select input) or its complement, as required for the function, then you can halve the multiplexer size. So an 8-input mux (plus an inverter) for any function of 4 bits.