Transcript Slide 1

BOOLEAN LOGIC AND GATES
BUILDING COMPUTER CIRCUITS
CONTROL CIRCUITS
prepared by Burak Galip ASLAN ([email protected])
September, 2006
Boolean logic
• Based on symbolic logic
TRUE
Binary 1
FALSE
Binary 0
1815 – 1864
English mathematician and logician
• An expression that results in a value of either
TRUE or FALSE
Boolean expression
2<5
a>7
Some Boolean operators
AND
OR
NOT
p
q
p.q
p
q
p+q
p
~p
T
T
T
T
T
T
T
F
T
F
F
T
F
T
F
T
F
T
F
F
T
T
F
F
F
F
F
F
inputs
output
binary operators
unary
operator
Gates
gate
• An electronic device that operates on a
collection of binary inputs to produce a binary
output
AND gate (from two transistors)
OR gate (from two transistors)
NOT gate (one transtistor)
Building computer circuits
• A collection of gates that transforms a set of
binary inputs into a set of binary outputs, and
the values of the outputs depend only on the
current values of the inputs
combinational circuit
Building computer circuits
sequential circuit
A circuit construction algorithm
construct truth table
construct sub-expression
with AND & NOT gates
For
each
output
column
construct sub-expression
with OR gates
construct circuit diagram
sum-of-products algorithm
Control circuits
multiplexer
Control circuits
decoder
Control circuits
multiplexer
decoder
http://home.wlu.edu/~lambertk/webinvitation/logic/logic.html
Summary
• What is Boolean logic?
• Relation between Boolean logic and gates
• Combinational circuits (an introduction)
References
• An Invitation to Computer Science,
1st Edition (1995) (Schneider & Gersting)
(Section 4.2)
• Wikipedia & Google
September, 2006