Module 2 Exercises CESC 220 Digital Circuit Design 1. Simplify the expression X'Y'Z + (X'Y'Z)' by applying one of the theorems. 2. Simplify the expression (AB' + CD)(B'E + CD) by applying one of the theorems. 3. Simplify the expression ACF + AC'F by applying one of the theorems. 4. Simplify the expression A(C + D'B) + A' by applying one of the theorems. 5. Factor the expression AB + C'D' to obtain a product of sums. 6. Factor the expression WX + WY'X + ZYX to obtain a product of sums. 7. Factor the expression A'BC + EF + DEF' to obtain a product of sums. 8. Factor the expression XYZ + W'Z + XQ'Z to obtain a product of sums. 9. Simplify the expression (A' + B' + C)(A' + B' + C)' by applying one of the theorems. 10. Simplify the expression AB(C' + D) + B(C' + D) by applying one of the theorems. 11. Simplify the expression AB + (C' + D)(AB)' by applying one of the theorems. 12. Simplify the expression (A'BF + CD')(A'BF + CEG) by applying one of the theorems. 13. Simplify the expression (X + Y'Z) + (X + Y'Z)' by applying one of the theorems. 14. Simplify the expression [W + X'(Y + Z)][W' + X'(Y + Z)] by applying one of the theorems. 15. Simplify the expression (V'W + UX)'(UX + Y + Z + V'W) by applying one of the theorems. 16. Simplify the expression (UV' + W'X)(UV' + W'X + Y'Z) by applying one of the theorems. 17. Factor the expression A'B' + A'CD + A'DE' to obtain a product of sums. 18. Factor the expression H'I' + JK to obtain a product of sums. 19. Factor the expression A'BC + A'B'C + CD' to obtain a product of sums. 20. Factor the expression A'B' + (CD' + E) to obtain a product of sums. 21. Factor the expression W + U'YV to obtain a product of sums. 22. Factor the expression TW + UY' + V to obtain a product of sums. 23. Find a sum-of-products expression for F' for the function F(P, Q, R, S) = (R' + PQ)S 24. Simplify (A + B' + C + E')(A + B' + D' + E)(B' + C' + D' + E') algebraically to a minimum sum of products (five terms). 25. Factor K'L'M + KM'N + KLM + LM'N' to obtain a product of sums (four terms). 26. Factor KL + K'L' + L'M'N' + LMN' to obtain a product of sums (four terms). 27. Factor KL + K'L'M + L'M'N + LM'N' to obtain a product of sums (four terms). 28. Determine if the equation a'b + b'c + c'a = ab' + bc' +ca' is valid. 29. Determine if the equation (a + b)(b + c)(c + a) = (a' + b')(b' + c')(c' + a') is valid. 30. Determine if the equation abc + ab'c' + b'cd + bc'd + ad = abc + ab'c' + b'cd + bc'd is valid. 31. Determine if the equation xy' +x'z + yz' = x'y + xz' + y'z is valid. 32. Is the statement \"If A + B = C, then AD' + BD' = CD'\" always true? 33. Is the statement \"If A'B + A'C = A'D, then B + C = D'\" always true? 34. Given: F(a, b, c) = abc' + b'. (a) Express F as a minterm expansion (Use m-notation): F = (b) Express F as a maxterm expansion (Use M-notation): F = (c) Express F' as a minterm expansion (Use m-notation): F' = (d) Express F' as a maxterm expansion (Use M-notation): F' = 35. Given: F(a, b, c, d) = (a + b + d)(a' + c)(a' + b' + c')(a + b + c' + d') (a) Express F as a minterm expansion (Use m-notation): F = (b) Express F as a maxterm expansion (Use M-notation): F = (c) Express F' as a minterm expansion (Use m-notation): F' = (d) Express F' as a maxterm expansion (Use M-notation): F' = Page 2 of 2