Combinational Circuits

• Logic Gates

Building a Circuit

Using Minterms/Maxterms

1. Define a functional specification (input/output)
2. Translate specification to a truth table
3. Derive a boolean expression, simplify
   • Use minterm: Product (AND) of inputs that produces a specific output, combine with OR
   • Use maxterm: Sum (OR) of inputs that produces a specific output, combine with AND
   • Minterm = Negation of maxterm
4. Implement boolean expression with combination of nodes (logic gates)

Using Karnaugh Map

1. Define a functional specification (input/output)
2. Translate specification to a truth table
3. Draw a Karnaugh Map
4. Convert Karnaugh Map to a boolean expression
5. Implement boolean expression

Boolean Algebra Properties

Bubble Pushing

Infer circuit’s equation by inspection

• Start at the output, work toward the inputs
• Draw each gate in a way that the bubbles cancel (A NOR B becomes !A OR !B, cancel negations)