Simplification and Boolean Expression

Core Computer Science For the IB Diploma Program by Kostas Dimitriou, Markos Hatzitaskos

Examples and calculations and showing each property:

Example 1:

Y = A’B(A + B’) + AB’(A’ + B) + AB(A’ + B’)

Break it down into three parts:

1. Apply the Distributive property for the whole equation. Apply the property in each part. If you do so, you should get:

2. Using the idea of using the Complement property, arrange it into the form of the Commutative property. So now, what’s inside the brackets is in the form of the Complement law. When applied to one part, do the same for the other two parts. When done so, it should look like this:

3. Simplify further now that we know that the Complement property is used.

4. Use the Null property to simplify.

And with that, the final outcome would be: 0.

Example 2:

Example 3:

Example 4: