ECE 3110: Introduction to Digital Systems

1. ECE 3110: Introduction to Digital Systems Combinational Logic Design Principles

2. Previous… • Principle of duality • N-variable theorems • Finite induction • Demorgan theorems

3. DeMorgan Symbol Equivalence

4. Likewise for OR

5. DeMorgan Symbols

6. Truth Table • Basic representation of a logic function. • Lists the output for every possible input combination. • n-variable logic function has a truth table with 2n rows.

8. More definitions (Sec. 4.1.6) • Literal: a variable or the complement of a variable • Product term: Z,X’, X.Y, X.W.Y’ • Sum-of-products expression: Z+X’.Y+X.W.Y’ • Sum term: Z, X’, W+X+Y’ • Product-of-sums expression: Z’.(X+Y) .(W+X+Y’) • Normal term: W+X’+Y, W.X.Y • Minterm (n variables): normal product term • Maxterm (n variables): normal sum term

9. Truth table vs. minterms & maxterms Minterm number, maxterm number

10. Other representations • Minterm list • on-set: each minterm turns on the output for exactly one input combination • Canonical sum: • Maxterm list • off-set: each maxterm turns off the output for exactly one input combination • Canonical product

11. Representations of Logic Functions Truth table Canonical sum [e.g. X’.Y’+X.Y] Minterm list: on-set Canonical product [e.g. (X’+Y).(X+Y’) ] Maxterm list: off-set Representations for a combinational logic function

12. Next… • Read Chapter 4.3 and take notes • Combinational circuit Synthesis