Example Question: Consider the expressions: (a) F = XY + XY'

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Presentation transcript:

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

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

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) X Y F 0 x 0 1 x 1 2 iii. Implement the logic circuit X F = X

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

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

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) 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 iii. Implement the logic circuit X Y Y' XY X'Y' B = XY + X'Y' X' 3 Simplify the expression using Karnaugh map 1 X YZ 00 01 11 10 B = X'Y' + XY

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

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) 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 iii. Implement the logic circuit W Z D = W'Z' 3 Simplify the expression using Karnaugh map 1 WX YZ 00 01 11 10 D = W'Z'