ELEC151 Digital Circuits and Systems
Ho-Chi Huang, Lecture Notes, No. 2-1
Lecture Note #2
Boolean Algebra
•
Basic definitions and axioms
2-1, 2-2
•
Laws and theorems of Boolean algebra
2-3, 2-4
– Design process and Boolean algebra
•
Two-level canonical forms
2-5
– Incompletely specified functions
•
More logic functions
2-6, 2-7
– NOT, AND, OR, NAND, NOR, XOR, XNOR, and more
– Positive and negative logic
•
Integrated circuits
2-8
– CMOS, TTL, …
– OrCAD (in laboratory)
•
Reading Assignments:
– Chapter 2
ELEC151 Digital Circuits and Systems
Ho-Chi Huang, Lecture Notes, No. 2-2
Boolean Algebra/Logic Circuits
•
Boolean Algebra
– In 1854, a mathematician,
George Boole
, developed
an algebraic system to handle only two variables,
TRUE and FALSE
•
Digital Circuits
– In 1938,
Claude Shannon
(father of information
theory) showed (in his Master’s thesis!) how to map
Boolean Algebra to digital circuits:
•
Structure of Boolean Algebra
– A set of elements
B
– Two binary operators, AND (•) and OR (+)
– One unary operator, NOT (’)
•
Primitive Gates
– AND, OR and NOT
ELEC151 Digital Circuits and Systems
Ho-Chi Huang, Lecture Notes, No. 2-3