1. ECE 2110: Introduction to Digital Systems
Combinational Logic Design Principles

2. Combinational logic circuit
Outputs depend only on the current inputs (Not on history)
Contain an arbitrary number of logic gates and inverters, but NO feedback loops.

3. Combinational-Circuit Analysis
Kinds of combinational analysis:
exhaustive (truth table)
algebraic (expressions)
simulation / test bench ( not in this course)
Write functional description in HDL
Define test conditions / test vectors
Compare circuit output with functional description (or known-good realization)
Repeat for “random” test vectors

4. Switching algebra “Boolean algebra” Positive-logic convention
deals with Boolean values -- 0, 1
Positive-logic convention
analog voltages LOW, HIGH --> 0, 1
Negative logic -- seldom used
Signals denoted by symbolic variables (X, Y, FRED, etc.)

5. Boolean operators Complement: X¢ (opposite of X) AND: X × Y OR: X + Y
binary operators, described functionally by truth table.

6. Logic symbols

7. Some definitions Literal: a variable or its complement
X, X¢, FRED¢, CS_L
Expression: literals combined by AND, OR, parentheses, complementation
X+Y
P × Q × R
A + B × C
((FRED × Z¢) + CS_L × A × B¢ × C + Q5) × RESET¢
Equation: Variable = expression
P = ((FRED × Z¢) + CS_L × A × B¢ × C + Q5) × RESET¢

8. Axioms (postulates) Logic multiplication and addition precedence
A1) X=0 if X‡ A1’ ) X=1 if X‡0
A2) if X=0, then X’=1 A2’ ) if X=1, then X’=0
A3) 0 • 0= A3’ ) 1+1=1
A4) 1 • 1= A4’ ) 0+0=0
A5) 0 • 1= 1 • 0 = A5’ ) 1+0=0+1=1
Logic multiplication and addition
precedence

9. Theorems (Single variable)
Proofs by perfect induction

10. Two- and three- variable Theorems

11. Summary Variables, expressions, equations Axioms (A1-A5 pairs)
Theorems (T1-T11 pairs)
Single variable
2- or 3- variable
Prime, complement, logic multiplication/addition, precedence

12. Next… Chapter 4.1,4.2 N-variable theorem, DeMorgan’s theorems
Standard representations of logic functions
HW #4