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BOOlean Logic The basis for digital electronics. What digital electronics do you use? Computer CD & DVD players IPod Cell phone HDTV Digital cameras What are digital electronics? Sound is an analog signal. On a CD, digital sound is encoded as 44.1 kHz, 16 bit audio.

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boolean logic

BOOlean Logic

The basis for digital electronics.

what digital electronics do you use
What digital electronics do you use?
  • Computer
  • CD & DVD players
  • IPod
  • Cell phone
  • HDTV
  • Digital cameras
what are digital electronics
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
george boole
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.
have you used boolean logic
Have you used Boolean logic?
  • What information have you searched for on the Web?
  • Do a Google Search for car radios.
the and operator both all
The AND operator (both, all)
  • rivers AND salinity
  • dairy products AND export AND Europe
the or operator either any
The OR operator (either, any)
  • fruit OR vegetables
  • fruit OR vegetables OR cereal

from CSIRO Australia

the not operator
The NOT operator
  • fruit NOT apples
  • Look at the Boolean Machine http://kathyschrock.net/rbs3k/boolean/
let s use boolean logic to examine class
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.
nesting
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 ORwhen there is any other operator in the search.
order of precedence of boolean operators
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.
write out logic statements using boolean operators for these
Write out logic statements using Boolean operators for these.
  • You have a buzzer in your car that sounds when your keys are in the ignition and the door is open.
  • You have a fire alarm installed in your house. This alarm will sound if it senses heat or smoke.
  • There is an election coming up. People are allowed to vote if they are a citizen and they are 18.
  • To complete an assignment the students must do a presentation or write an essay.
basis for digital computers
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
not gate
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.

From How Stuff Works

and gate
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).
or gate
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.
  • http://www.play-hookey.com/digital/basic_gates.html
combine gates
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.
all computations can be done with an nand gate
All computations can be done with an NAND gate.
  • The most sophisticated computer can be made with NAND gates from Radio Shack.
  • Need millions of them.
how do we use gates to add two binary numbers
How do we use gates to add two binary numbers?
  • Binary numbers are either 1 or 0, either on or off.
  • Have two outputs.
  • Need a gate to produce each output.
how do i add larger numbers
How do I add larger numbers?
  • You can write any number in binary.
add binary numbers
Add binary numbers.
  • Adding larger number just adds more columns.
gang circuits in sequence
Gang circuits in sequence.
  • To construct a full adder circuit, we'll need to gang these simple circuits together.
  • The “carry” value will become an input for the subsequent
  • Now have three inputs and two outputs.
  • Since we'll have both an input carry and an output carry, we'll designate them as CIN and COUT.
different version of full adder
Different Version of Full Adder.
  • Now we can add two binary bits together
    • accounting for a possible carry from the next lower order of magnitude.
    • sending a carry to the next higher order of magnitude.
add multiple bits
Add multiple bits.
  • A full adder must be allocated for each bit to be added simultaneously.
  • To add two 4-bit numbers to produce a 4-bit sum (with a possible carry), you would need four full adders with carry lines cascaded.
  • By extension, two binary numbers of any size may be added in this manner.
  • http://www.play-hookey.com/digital/adder.html
gates from electrical relays
Gates from electrical relays.
  • NOT gate
  • AND gate
  • OR gate
test your knowledge on boolean logic
Test your knowledge on Boolean logic.
  • http://educ.queensu.ca/~compsci/resources/BoolLogic/assocdistrib.html
here is a great resource for digital electronics
Here is a great resource for digital electronics.
  • http://hyperphysics.phy-astr.gsu.edu/Hbase/electronic/digcktcon.html#c1
exclusive gates
“Exclusive” gates
  • Exclusively OR gate are true if either input is true but not both.