Microprocessors vs. Custom Digital Circuits

1
Microprocessors vs. Custom Digital Circuits
Designers that work with digital phenomena often
buy an off-the-shelf microprocessor and program
it.
Microprocessors are readily available,
inexpensive, easy to program, and easy to
reprogram
Why would anyone ever need to design new digital
circuits?
2
Microprocessors vs. Custom Digital Circuits
Designers that work with digital phenomena often
buy an off-the-shelf microprocessor and program
it.
Microprocessors are readily available,
inexpensive, easy to program, and easy to
reprogram
Why would anyone ever need to design new digital
circuits?

• Microprocessors are sometimes
• Too slow
• Too big
• Consume too much power
• Too costly

3
Combinatorial Logic Circuits
A digital circuit whose output depends solely on
the present combination of input values is called
a combinatorial circuit
Logic gates building blocks of logic circuits
AND OR NOT
Boolean Algebra
Boolean algebra is a branch of mathematics that
uses variables whose values can only be 1 or 0
(true or false, respectively) and whose
operators, like AND, OR, NOT, operate on such
variables and return 1 or 0.
We can build circuits by doing math
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Logic Gates
Truth Tables
Example Seatbelt warning light
Design a system for an automobile that
illuminates a warning light whenever the drivers
seatbelt is not fastened, and the key is in the
ignition
Boolean equation w NOT(s) AND k
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Notation and Terminology

• Operators
• NOT(a) is typically written as a
• a OR b is typically written as a b
• a AND b is typically written as a b (or a b)

w NOT(s) AND k sk

• Precedence rule
• Expression in parentheses
• AND, NOT
• OR

w (a b) (c) d
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Properties of Boolean Algebra

• Commutative
• a b b a
• a b b a
• Distributive
• a (b c) a b a c
• a (b c) (a b) (a c)
• Associative
• (a b) c a (b c)
• (a b) c a (b c)
• Identity
• 0 a a 0 a
• 1 a a 1 a
• Complement
• a a 1
• a a 0

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Additional Properties

• Null elements
• a 1 1
• a 0 0
• Idempotent Law
• a a a
• a a a

• Involution Law
• (a) a
• De Morgans Law
• (a b) a b
• (a b) a b

Example Simplification of an automatic sliding
door system
f h c h p c
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Additional Properties

• Null elements
• a 1 1
• a 0 0
• Idempotent Law
• a a a
• a a a

• Involution Law
• (a) a
• De Morgans Law
• (a b) a b
• (a b) a b

Example Simplification of an automatic sliding
door system
f h c h p c
f c (h p)
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Boolean Functions
Boolean function is a mapping of each possible
combination of input values to either 0 or 1.
Boolean function can be represented as an
equation, a circuit, and as a truth table.
Converting a truth table to an equation
F a b a
F a b a b a b
For any function, there may be many equivalent
equations, and many equivalent circuits, but
there is only one truth table!