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'

Example

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 Algebraii. 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 ii. Implement the logic circuit

1 i. Build the truth table

X Y F0 0 00 1 01 0 11 1 1

X

Y

Y'

XY

XY'

F = XY + XY'

Question: (a) F = XY + XY'

2 ii. Build the truth table (of the simplified expression)

2 i. Simplify the expression using theorems of Boolean Algebra

F = XY + XY'= X(Y + Y')= X . 1= X

X Y F0 x 01 x 1

2 iii. Implement the logic circuit

X F = X

Question: (a) F = XY + XY'

3 Simplify the expression using Karnaugh map

0X

Y

0

11

0 1

0

1

F = X

Question: (b) B = XYZ + XYZ' + X'Y'Z + X'Y'Z'

1 i. Build the truth table

X Y Z B0 0 0 10 0 1 10 1 0 00 1 1 01 0 0 01 0 1 01 1 0 11 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 ii. Build the truth table (of the simplified expression)

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'

X Y Z B0 0 x 10 1 x 01 0 x 01 1 x 1

2 iii. Implement the logic circuit

Question: (b) B = XYZ + XYZ' + X'Y'Z + X'Y'Z'

X

Y

Y'

XY

X'Y'

B = XY + X'Y'

X'

3 Simplify the expression using Karnaugh map

B = X'Y' + XY

1X

YZ

1

00

00 01

0

1

0 0

11

11 10

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 B0 0 0 0 10 0 0 1 00 0 1 0 10 0 1 1 00 1 0 0 10 1 0 1 00 1 1 0 10 1 1 1 01 0 0 0 01 0 0 1 01 0 1 0 01 0 1 1 01 1 0 0 01 1 0 1 01 1 1 0 01 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 ii. Build the truth table (of the simplified expression)

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'

W X Y Z D0 x x 0 10 x x 1 01 x x 0 01 x x 1 0

2 iii. Implement the logic circuit

Question: (c)D = W'X'Y'Z' + W'X'YZ' + W'XY'Z' + W'XYZ'

3 Simplify the expression using Karnaugh map

D = W'Z'

W

Z

D = W'Z'

1WX

YZ

0

01

00 01

00

01

0 1

10

11 10

0 0

00

11

10

0 0

00