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Question: Consider the expressions: (a) F = XY + XY' (b) B = XYZ + XYZ' + X'Y'Z + X'Y'Z'

Example. Question: Consider the expressions: (a) F = XY + XY' (b) B = XYZ + XYZ' + X'Y'Z + X'Y'Z' (c) D = W'X'Y'Z' + W'X'YZ' + W'XY'Z' + W'XYZ'. For each of these expressions, 1 i. Build the truth table ii. Implement the logic circuit

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Question: Consider the expressions: (a) F = XY + XY' (b) B = XYZ + XYZ' + X'Y'Z + X'Y'Z'

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  1. Example Question: Consider the expressions: (a) F = XY + XY' (b) B = XYZ + XYZ' + X'Y'Z + X'Y'Z' (c) D = W'X'Y'Z' + W'X'YZ' + W'XY'Z' + W'XYZ' For each of these expressions, 1 i. Build the truth table ii. Implement the logic circuit 2 i. Simplify the expression using theorems of Boolean Algebra ii. Build the truth table (of the simplified expression) iii. Implement the logic circuit 3 Simplify the expression using Karnaugh map

  2. X Y F 0 0 0 0 1 0 1 0 1 1 1 1 X XY Y F = XY + XY' Y' XY' Question: (a) F = XY + XY' 1 i. Build the truth table 1 ii. Implement the logic circuit

  3. X Y F 0 x 0 1 x 1 X F = X Question: (a) F = XY + XY' 2 i. Simplify the expression using theorems of Boolean Algebra F = XY + XY' = X(Y + Y') = X . 1 = X 2 ii. Build the truth table (of the simplified expression) 2 iii. Implement the logic circuit

  4. Y 0 1 X 0 0 0 1 1 1 Question: (a) F = XY + XY' 3 Simplify the expression using Karnaugh map F = X

  5. X Y Z B 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 Question: (b) B = XYZ + XYZ' + X'Y'Z + X'Y'Z' 1 i. Build the truth table

  6. X Y Z X' Y' Z' XYZ XYZ' B = XYZ + XYZ' + X'Y'Z + X'Y'Z' X'Y'Z X'Y'Z' Question: (b) B = XYZ + XYZ' + X'Y'Z + X'Y'Z' 1 ii. Implement the logic circuit

  7. X Y Z B 0 0 x 1 0 1 x 0 1 0 x 0 1 1 x 1 Question: (b) B = XYZ + XYZ' + X'Y'Z + X'Y'Z' 2 i. Simplify the expression using theorems of Boolean Algebra B = XYZ + XYZ' + X'Y'Z + X'Y'Z' = XY(Z + Z') + X'Y'(Z + Z') = XY + X'Y' 2 ii. Build the truth table (of the simplified expression)

  8. YZ X XY 00 01 11 10 X Y B = XY + X'Y' 1 1 0 0 0 1 0 0 1 1 X' Y' X'Y' Question: (b) B = XYZ + XYZ' + X'Y'Z + X'Y'Z' 2 iii. Implement the logic circuit 3 Simplify the expression using Karnaugh map B = X'Y' + XY

  9. W X Y Z B 0 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 0 Question: (c) D = W'X'Y'Z' + W'X'YZ' + W'XY'Z' + W'XYZ' 1 i. Build the truth table

  10. W X Y Z W' X' Y' Z' W'X'Y'Z' W'X'YZ' D = W'X'Y'Z' + W'X'YZ' + W'XY'Z' + W'XYZ' W'XY'Z' W'XYZ' Question: (c) D = W'X'Y'Z' + W'X'YZ' + W'XY'Z' + W'XYZ' 1 ii. Implement the logic circuit

  11. W X Y Z D 0 x x 0 1 0 x x 1 0 1 x x 0 0 1 x x 1 0 Question: (c) D = W'X'Y'Z' + W'X'YZ' + W'XY'Z' + W'XYZ' 2 i. Simplify the expression using theorems of Boolean Algebra D = W'X'Y'Z' + W'X'YZ' + W'XY'Z' + W'XYZ' = W'Z'(X'Y' + X'Y + XY' + XY) = W'Z'((X'(Y' + Y) + X(Y' + Y)) = W'Z'(X' + X) = W'Z' 2 ii. Build the truth table (of the simplified expression)

  12. W D = W'Z' Z YZ 00 01 11 10 WX 1 0 0 1 00 01 1 0 0 1 0 0 0 0 11 10 0 0 0 0 Question: (c) D = W'X'Y'Z' + W'X'YZ' + W'XY'Z' + W'XYZ' 2 iii. Implement the logic circuit 3 Simplify the expression using Karnaugh map D = W'Z'

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