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. 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'

3. 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

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

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

6. 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'

7. 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

8. 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

9. 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

10. 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'

11. 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

12. 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'