Cells and Hierarchy - input and output ports, interconnects, top down and bottom up design.

Hierarchical levels - silicon IC --> CMOS circuit --> logic gates --> logic components --> system

Binary Logic - binary variables that take on two discrete values and mathematical logic operations applied to these variables

Basic logic operations

•     NOT
•     AND
•     OR

Gates - electronic implementations of logic operators.

• 2-input gates
• multi-input gates

Switching functions - (logic functions, boolean expressions)  - functions of boolean variables. Implemented with connections between logic gates.

Truth tables can be used to define switching functions as well.

Logic diagrams -  illustrations of switching function implementations.

    Example: Given logic diagram, find function.

    Example: Given function, find logic diagram.

Boolean Algebra - the formal algebraic system dealing with binary variables and logic operations.

Basic Identities
 

OR form	AND form
1. X + 0 = X	2. X . 1 = X
3. X + 1 = 1	4. X . 0 = 0
5. X + X = X	6. X . X = X
7. X + X' = 1	8. X . X' = 0
9. (X')' = X
10. X + Y = Y + X	11. XY = YX	Commutative
12. X + (Y + Z) = (X + Y) + Z	13. X(YZ) = (XY)Z	Associative
14. X(Y + Z) = XY + XZ	15. X + YZ = (X + Y)(X + Z)	Distributive
16. (X + Y)' = X' . Y'	17. (XY)' = X' + Y'	DeMorgan's

Duality - the dual of a function is found by interchanging OR and AND operations and replacing 1's and 0's by 0's and 1's.

Complements of Functions - use of DeMorgan's Law  

NAND and NOR gates

• truth tables
• gate symbols
• gate equivalents
  • AND = NOR with inverted inputs
  • OR = NAND with inverted inputs