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BUILDING COMPUTER CIRCUITS
prepared by Burak Galip ASLAN ([email protected])
September, 2006
BOOLEAN LOGIC AND GATES
CONTROL CIRCUITS
Boolean logic
1815 – 1864 English mathematician and
logician
• Based on symbolic logic
TRUE FALSE
Binary 1 Binary 0
• An expression that results in a value of either TRUE or FALSE
Boolean expression
2 < 5 a > 7
Some Boolean operators
p q p + q
T T T
T F T
F T T
F F F
p q p . q
T T T
T F F
F T F
F F F
p ~ p
T F
F T
ORAND NOT
inputs output
binary operatorsunary
operator
Gates
• An electronic device that operates on a collection of binary inputs to produce a binary output
gate
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
construct sub-expression with OR gates
construct circuit diagram
sum-of-products algorithm
For each
output column
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)
• An Invitation to Computer Science, 1st Edition (1995) (Schneider & Gersting) (Section 4.2)
• Wikipedia & Google
September, 2006
References
