1. Simplify the following Boolean Algebra equations by applying De Morgan's Theorem and other algebraic manipulations and then generate a truth table for each of them to confirm that your expression is minimal (30 points): a F(X,Y,Z,W) = (XYZW + XZ) + YZW b. F(A,B,C) = AB (A + BC + CAC + AB) c f(a, b,c) = a (a' bc' + ab'c + (b + c)') 2. Convert the equations to sum-of-minterms (20 points): a F(x, y, z, w) = yw + xyz + xz b. F(A,B,C,D) = C (A + BC + D + BD) 3. Find the simplified expressions given the K-maps (20 points): * In the last two parts d means don't cares a. F(A,B,C,D) = m(3,7,11,14,15) CD CD CD CD" | 2. F(x, y, z, w) = (1,4,5,6,7,9,14) " CD CD CD" c. F(A,B,C,D) = 2m(1,5,6,9,14) + d(3,4,7) 'D' CD CD CD" d. F(A, B,C,D) = (0,4,8,13) +d(1,3,5,7) CD CD CD CD" 4. Represent the equation using the Universal Gates (10 points) F(x, y, z) = xy + iz + zxy 5. Implement part 'a' of question 3 using a 4 to 16 decoder and minimal other gates (10 points). 4-16 Decoder 6. Implement part 'b' of question 3 using an 8 to 1 multiplexor and minimal other gates (10 points) 8 to 1 MUX S2 S1 SO