Download Combinational Logic

Combinational Logic
An Overview
Digital Electronics
Combinational Logic
This presentation will
• Introduce the basics of combinational and
sequential logic.
• Present the logic symbol, logic expression, and
truth table for the AND gate, OR gate, and
INVERTER gate.
• Review the design for a simple combinational logic
circuit.
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Combinational & Sequential Logic
Combinational
Logic
Sequential
Logic
Inputs
.
.
.
Inputs
.
.
Clock
Combinational
Logic Gates
Combinational
Logic Gates
Memory
Elements
(Flip-Flops)
.
.
.
Outputs
.
.
Outputs
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General Form for All Logic Gates
Logic Symbol
Output
X
Y
Z=XY
Inputs
Logic Expression
X Y Z
0
0 1
Truth Table
0
1 0
1
0 1
1
1 1
Lists the output
condition for all
possible input
combinations.
PS – There’s no such thing as a smiley face gate.
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The AND Gate
X
Y
Z  X  Y  X  Y  XY
X Y Z
0
0 0
0
1 0
1
0 0
1
1 1
Three ways
to write the
AND symbol
Z is TRUE whenever X AND Y are TRUE
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The OR Gate
X
Y
Z XY
X Y Z
0
0 0
0
1 1
1
0 1
1
1 1
Z is TRUE whenever X OR Y are TRUE
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The INVERTER Gate
The NOT
symbol or bar
Z X
X
X Z
0 1
0 1
1 0
Z is TRUE whenever X is NOT TRUE
1 0
The inverter is sometimes called the NOT gate.
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AOI Logic
• Combinational logic designs implemented with AND
gates, OR gates, and INVERTER gates are referred to
as AOI designs.
A
ND
O
R
I
NVERT
• AOI Logic is just one type of combinational logic. Unit 2
of this course will spend a significant amount of time
exploring other forms of combinational logic and their
applications.
• The purpose of this introduction is to provide a basis of
understanding for the combinational logic subsection of
the Board Game Counter design.
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Combinational Logic Design Example
The following is a review of the design and operation of a
combinational logic circuit using AOI logic. This design
controls the safety buzzer in a car and was designed to the
following specifications:
The buzzer is On whenever the door is open OR the key
is in the ignition AND the seat belt is NOT buckled.
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Design Example: Truth Table
The buzzer is On whenever
• the door is open
• OR
• the key is in the ignition AND the seat belt is NOT buckled.
Car Buzzer – Truth Table
Seat Belt
Key
Door
Buzzer
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
Seat Belt
0 : Seat Belt is NOT Buckled
1 : Seat Belt is Buckled
Key
0 : Key is NOT in the Ignition
1 : Key is in the Ignition
Door
Buzzer
0 : Door is NOT Open
1 : Door is Open
0 : Buzzer is OFF
1 : Buzzer in ON
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Design Example: Circuit Design
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Design Example: Functional Test
(1 of 8)
Logic ‘1’
Logic ‘0’
Seat Belt
Key
Door
Buzzer
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
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Design Example: Functional Test
(2 of 8)
Logic ‘1’
Logic ‘0’
Seat Belt
Key
Door
Buzzer
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
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Design Example: Functional Test
(3 of 8)
Logic ‘1’
Logic ‘0’
Seat Belt
Key
Door
Buzzer
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
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Design Example: Functional Test
(4 of 8)
Logic ‘1’
Logic ‘0’
Seat Belt
Key
Door
Buzzer
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
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Design Example: Functional Test
(5 of 8)
Logic ‘1’
Logic ‘0’
Seat Belt
Key
Door
Buzzer
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
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Design Example: Functional Test
(6 of 8)
Logic ‘1’
Logic ‘0’
Seat Belt
Key
Door
Buzzer
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
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Design Example: Functional Test
(7 of 8)
Logic ‘1’
Logic ‘0’
Seat Belt
Key
Door
Buzzer
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
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Design Example: Functional Test
(8 of 8)
Logic ‘1’
Logic ‘0’
Seat Belt
Key
Door
Buzzer
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
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Design Example: IC Component View
1
2
1
2
3
1
2
3
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Design Example Using LEDs
LED – Light Emitting Diode
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LED – Light Emitting Diode
To Turn an LED ON
• The ANODE must be at a
higher voltage potential
(1.5v) than the
CATHODE.
• The amount of current
flowing through the LED
will determine how bright
it is.
CATHODE (‒)
(+) ANODE
← Current Flow
• The amount of current is
controlled by a series
resistor. (not shown)
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LED Examples
Logic 1
ANODE
CATHODE
 5 volts
The ANODE is at a higher voltage
potential than the CATHODE; the
LED is ON.
Logic 0
ANODE
The 180 resistor controls the
current that flows through the LED.
This in turn controls its brightness.
CATHODE
 0 volts
The ANODE is NOT at a higher
voltage potential than the
CATHODE; the LED is OFF.
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