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9. Use a 4-variable K-map like the one shown here to determine the simplified expression for each given equation, x = f(a,b,c,d). Show ab 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 circling challenges you can expect to encounter. a. x = a'b'c'd' + a'b'cd + a'bc'd' + a'bcd' + abc'd' + abcd' + ab'c'd' + ab'cd b. x = m1 + m3 + m4 + m5 + m6 +m7 + m9 + m11 + m12 +m14 ab c. x as defined by the K-map below; hint can be simplified into 2 circles cd 00 01 11 10 cd 00 01 11 10 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 00 01 11 10 00 01 11 10

Fig: 1