Combinational Logic

1. Boolean Algebra
   • Basic gates: and or not
   • Additional gates: Nand, nor, xor, xnor
   • Operator precedence
   • Evaluating a boolean equation
   • Terminology: variable, literal, product term, sum-of-products
   • Algebraic properties: commutative, distributative, associative, identity, complement, null elements, idempotent law, involution law, DeMorgan's law
   • Reduce functions using algebraic properties
2. Representations of Boolean Functions
   • Equations, circuits, truth tables
   • Converting between representations
3. Logic circuits
   • Drawing conventions for logic circuits
   • Converting a boolean equation to a logic circuit
4. Canonical Forms
   • Sum-of-minterms
5. Combinational logic design process
   1. Capture the function
   2. Convert to equations
   3. Implement as gate-level circuit
6. Understand common combinational functions
   • 1's count, detecting all 0's, detecting equality
   • decoder and multiplexer (mux)