I am trying to design a circuit.

F(a,b,c) = ab +c (if a=0,2,5,7,8)

F(a,b,c) = b +c (if a≠0,2,5,7,8)

a,c are 4bit binary numbers, b: 2bit number

I have to use multiplexers 2by1, full adders and logic gates.

I am trying to find a solution for the first part.

f1 = ab (if a...)..

f1: 6 bits

Karnaugh map for 6 bits I think is overkill. Is there any way to check the "a" with multiplexers?

Thank you.