Reduction of Switching Equations Using Boolean Algebra

· Idea

- Redundant terms should be eliminated because they add cost to the circuit.

F = XY’Z + XYZ = XZ(Y + Y’) = XZ

Example

1) P = X’YZ’ + X’YZ + XYZ’ + XYZ

= X’Y(Z + Z’) + XY(Z + Z’)

= X’Y + XY

= Y

2) S = A(B’ + C)’ * (BC)’

= A * (BC’) * (B’ + C’)

= A (BC’)

= ABC’