8. Use a 3-variable K-map like the one shown here to determine the simplified expression for each given equation, x = f(a,b,c). Show the K-map circles used to perform reduction and define the final, simplified equation for x. If an expression cannot be simplified by the K-map, explain why. These equations are chosen to show the variety of circles you can expect to encounter. a. x = a'b'c + a'bc + ab'c' + abc b. x = a'b'c' + a'b'c + a'bc' + a'bc + abc' + abc c. x = a'b'c' + a'bc' + ab'c' + ab'c + abc' (0) a bc 0 1 00 01 11 10

Fig: 1