Digital Logic Design
Truth Table Logic Circuit 1. Start with truth table 2. When your output is a 1, figure out the combination of inputs, ANDs, and NOTs Example:A = 0, B = 1, C = 0 A’·B·C’ A = 1, B = 1, C = 0 A·B·C’ 3. When you have all your “miniterms,” OR all of them together Example:f = A’·B·C’ + A·B·C’ 4. Simplify your boolean expression 5. Build your digital circuit
Example What is the boolean function for the truth table below? miniterms: A’·B’·C A’·B·C A·B’·C’ A·B’·C A·B·C f = A’·B’·C + A’·B·C + A·B’·C’ + A·B’·C + A·B·C ABCf
Example Simplify the boolean expression f = A’·B’·C + A’·B·C + A·B’·C’ + A·B’·C + A·B·C f = A’·C + A·B’ + A·B·C f = A’·C + A ( B’ + C ) Build the digital circuit from the simplified expression
Your Turn Design the digital circuit for the following truth table: ABCf
1) Get the Boolean expression? ABCf Hint: What are the miniterms?
2) Simplify! f = A’·B·C + A·B’·C’ + A·B’·C + A·B·C’ + A·B·C
3) Build the Digital Circuit f = A + B·C
Done! f = A + B·C