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Presentation on Boolean Algebra and Logic Gates
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Boolean algebra and logic
gates
George Boole
mathematician and logician
formalized logic in a mathematical manner
father of Boolean algebra and modern symbolic logic
George Boole
Boolean algebra
or Boolean logic
The Mathematical Analysis of Logic 1847.
defines relations between prepositions
mathematical calculus of truth values
C. E. Shannon
Boolean operators can be used in logic gates
Claude E. Shannon 1938.
a century after Boolean logic
revolution in informatics
Boolean algebra and logic gates
logic gates control the flow of electric current through integrated circuits
they control it based on Boolean algebra
True or 1 presence of electric tension
False or 0 absence of electric tension
Logic gates
atomic prepositions
+
logic operators
=
logic gates
Logic gates
Logic gate AND
A B AB
0 0 0
0 1 0
1 0 0
1 1 1
Logic gates
Logic gate OR
A B A+B
0 0 0
0 1 1
1 0 1
1 1 1
Logic gates
Logic gate NOT
A ~A
0 1
1 0
Logic gates
Logic gate NAND
A B ~(AB)
0 0 1
0 1 1
1 0 1
1 1 0
Logic gates
Logic gate NOR
A B ~(A+B)
0 0 0
0 1 1
1 0 1
1 1 1
Logic gates
other gates
XNAND
XNOR
MINTERM
MAXTERM
Logic gates
goal simplifying complex operations
why? faster, cheaper, smaller
how? researching and studying rules
no algorithms or shortcuts
Moores law
"The number of transistors incorporated in a chip will approximately double every 24
months."
computers
faster, smaller and better overall performance
Recapitulation
George Boole
Boolean algebra and modern symbolic logic
C. E. Shannon
Boolean algebra and integrated circuits
no modern computers without Boolean algebra
Questions
1. Name a logic operator and say when its
output value equals 0!
2. Who discovered that Boolean algebra
can be used for managing the flow of
electric current in integrated circuits?
3. What does Moores law say?
Any
questions?