The document discusses the basis of digital electronics in Boolean logic. It describes how British mathematician George Boole developed Boolean logic using the operators AND, OR, and NOT. Digital devices like computers use binary logic based on these Boolean operations to process true-false signals. Electronic circuits called gates perform the basic Boolean logic functions and can be combined to perform more complex operations.

1. The basis for digital electronics.

2. What digital electronics do you
use?
Computer
CD & DVD players
IPod
Cell phone
HDTV
Digital cameras

3. What are digital electronics?
Sound is an analog signal.
On a CD, digital sound is encoded
as 44.1 kHz, 16 bit audio.
 The original wave is 'sliced' 44,100
times a second - and an average
amplitude level is applied to each
sample.
 16 bit means that a total of 65,536
different values can be assigned, or
quantized to each sample.
DVD-Audio can be 96 or 192 kHz
and up to 24 bits resolution

4. George Boole
George Boole, a British mathematician (1815-1864).
Logic and math are equivalent.
All math functions can be determined using these 3
primary Boolean logic operators: AND, OR, and NOT.
AND narrows your search,
OR broadens your search, and
NOT is used to exclude concepts.

5. Have you used Boolean logic?
What information have you searched for on the Web?
Do a Google Search for car radios.

6. The AND operator
(both, all)
rivers AND salinity
dairy products AND export AND
Europe

7. The OR operator
(either, any)
fruit OR vegetables
fruit OR vegetables OR cereal
from CSIRO Australia

8. The NOT operator
fruit NOT apples

9. Let’s use Boolean logic to examine
class.
Please stand up if you are:
girl
AND black hair
AND left handed
Please stand up if you are:
girl
OR black hair
OR left handed
And NOT
How has the group changed depending on the logical
operator used.

10. What would a library search give
for “stress” and “anxiety”?
Shaded areas indicate
retrieval Search Statement Types of records retrieved
Number of
records
retrieved
stress OR anxiety Documents that discuss
either stress or anxiety 1127
stress AND anxiety Documents that discuss
both stress and anxiety 51
Documents that discuss

11. Nesting
When more than one element is in parentheses, the sequence is left to
right. This is called "nesting."
 (foxes OR rabbits) AND pest control
 foxes OR rabbits AND pest control
 (animal pests OR pest animals) NOT rabbits
Parentheses should be used to group terms joined by OR when there
is any other operator in the search.

12. Order of precedence of Boolean
operators
The order of operations is: AND, NOT, OR, XOR
Parentheses are used to override priority.
Expressions in parentheses are processed first.
Parentheses are used to organize the sequence and
groups of concepts.

13. Basis for digital
computers.
The true-false nature of Boolean
logic makes it compatible with
binary logic used in digital
computers.
Electronic circuits can produce
Boolean logic operations.
Circuits are called gates.
 NOT
 AND
 OR

14. NOT gate
 The simplest possible gate is called an "inverter," or a NOT gate.
 One bit as input produces its opposite as output.
 The symbol for a NOT gate in circuit diagrams is shown below.
 The logic table for the NOT gate shows input and output.
A Q
0 1
1 0
From How Stuff Works

15. AND gate
 The AND gate has the following symbol and logic
table.
 Two or more input bits produce one output bit.
 Both inputs must be true (1) for the output to be
true.
 Otherwise the output is false (0).
A B Q
0 0 0
0 1 0
1 0 0
1 1 1

16. OR gate
 The OR gate has the following symbol and logic table.
 Two or more input bits produce one output bit.
 Either inputs must be true (1) for the output to be true.
A B Q
0 0 0
0 1 1
1 0 1
1 1 1
 http://www.play-hookey.com/digital/basic_gates.html

17. Combine gates.
Gates can be combined.
The output of one gate can become the input of another.
Try to determine the logic table for this circuit.

18. Construct the logic table for these
circuits.