Transcript Chapter 02

Chapter 2
Logic Functions and Gates
Basic Logic Functions
• The three basic logic functions are:
– AND
– OR
– NOT
2
Logic Function Representation
• Logic functions can be represented:
–algebraically
–using truth tables
–using electronic circuits.
3
Algebraic Representation
• Uses Boolean algebra.
• Boolean variables have two states
(binary).
• Boolean operators include AND, OR,
and NOT.
4
Truth Table Representation
• Defines the output of a function for
every possible combination of inputs.
• A system with n inputs has 2n possible
combinations.
5
Electronic Circuit Representation
• Uses logic gates to perform Boolean
algebraic functions.
• Gates can be represented by schematic
symbols.
• Symbols can be either distinctive-shape
or rectangular-outline.
6
Distinctive Shape Schematic
Symbols
• Uses different graphic representations
for different logic functions.
• Uses a bubble (a small circle) to
indicate a logical inversion.
7
Rectangular-Outline Schematic
Symbols
• All functions are shown in rectangular
form with the logic function indicated by
standard notation inside the rectangle.
• The notation specifying the logic
function is called the qualifying symbol.
• Inversion is indicated by a 1/2
arrowhead.
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NOT Function
• One input and one output.
• The output is the opposite logic level of
the input.
• The output is the complement of the
input.
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NOT Function Boolean
Representation
• Inversion is indicated by a bar over the
signal to be inverted.
YA
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NOT Function Electronic Circuit
• Called a NOT gate or, more usually, an
INVERTER.
• Distinctive-shape symbol is a triangle
with inversion bubble.
• Rectangular-shape symbol uses “1” and
the inversion 1/2 arrowhead.
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NOT Function Electronic Circuit
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AND Function
• Two or more inputs, one output.
• Output is HIGH only when all of the
inputs are HIGH.
• Output is LOW whenever any input is
LOW.
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AND Function
A
B
Y
0
0
0
0
1
1
1
0
1
0
0
1
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AND Boolean Representation
• AND symbol is “•” or nothing at all.
Y  A B
Y  AB
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AND Function Electronic Circuit
• Called an AND gate.
• Distinctive-shape symbol uses AND
designation.
• Rectangular-shape symbol use “&” as
designator.
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AND Function Electronic Circuit
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AND Function Electronic Circuit
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AND Function Electronic Circuit
A
B
C
Y
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
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OR Function
• Two or more inputs, one output.
• Output is HIGH whenever one or more
input is HIGH.
• Output is LOW only when all of the
inputs are LOW.
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OR Function
A
B
Y
0
0
0
0
1
0
1
0
1
1
1
1
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OR Boolean Representation
• OR symbol is “+”.
• Y=A+B
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OR Function Electronic Circuit
• Called an OR gate.
• Distinctive-shape symbol uses OR
designation.
• Rectangular-shape symbol uses “” as
designator.
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OR Function Electronic Circuit
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Active Level
• The logic level defined as “ON” for a
circuit.
• When a logic HIGH is “ON”, the signal is
active-HIGH.
• When a logic LOW is “ON”, the signal is
active-LOW.
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NAND Function
• Generated by inverting the output of the
AND function.
• Output is HIGH whenever any input is
LOW.
• Output is LOW only when all inputs are
HIGH.
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NAND Function
A
B
Y
0
0
1
0
1
1
1
0
1
1
1
0
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NAND Boolean Representation
• Uses AND with an inversion overbar.
Y  A B
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NAND Function Electronic Circuit
• Called a NAND gate.
• Uses the AND symbol with inversion on.
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NAND Function Electronic Circuit
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NOR Function
• Generated by inverting the output of the
OR function.
• Output is HIGH only when all inputs are
LOW.
• Outputs is LOW whenever any input is
HIGH.
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NOR Function
A
B
Y
0
0
1
0
1
0
1
0
0
1
1
0
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NOR Boolean Representation
• Uses OR with an inversion overbar.
Y  A B
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NOR Function Electronic Circuit
• Called a NOR gate.
• Uses OR symbol with inversion on the
output.
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NOR Function Electronic Circuit
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3 Input NOR and NAND Function
Truth Tables
• 3 Input NAND: Y  A  B  C
• 3 Input NOR: Y  A  B  C
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3 Input NOR and NAND Function
Truth Tables
A B C
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
A BC
A BC
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
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Exclusive OR Gate
• Two inputs, one output.
• Output is HIGH when one, and only
one, input is HIGH.
• Output is LOW when both inputs are
equal – both HIGH or both LOW.
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Exclusive OR Gate
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Exclusive OR Gate
A
B
Y
0
0
0
0
1
1
1
0
1
1
1
0
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Exclusive NOR Gate
• Two inputs, one output.
• Output is HIGH when both inputs are
equal – both HIGH or both LOW.
• Output is LOW when one, and only one,
input is HIGH.
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Exclusive NOR Gate
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Exclusive NOR Gate
A
B
Y
0
0
1
0
1
0
1
0
0
1
1
1
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Gate Equivalence – NAND
• A NAND gate can be represented by an
AND gate with inverted output.
• A NAND gate can be represented by an
OR gate with inverted inputs.
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Gate Equivalence – NAND
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Gate Equivalence – NOR
• A NOR gate can be represented by an
OR gate with inverted output.
• A NOR gate can be represented by an
AND gate with inverted inputs.
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Gate Equivalence – DeMorgan
Forms
• Change an AND function to an OR
function and an OR function to an AND
function.
• Invert the inputs.
• Invert the outputs.
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DeMorgan’s Theorem - 1
A B  A  B
•
A B  A  B
•
• Break the line and change the sign
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DeMorgan’s Theorem - 2
• The following are two common errors
associated with DeMorgan’s Theorem:
• A B  A  B
• A B  A  B
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Active Logic Levels
• Any INPUT or OUTPUT that has a
BUBBLE is considered as active LOW.
• Any INPUT or OUTPUT that has no
BUBBLE is considered as active HIGH.
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Active Logic Levels - NOR
• Y  A B
• At least one input HIGH makes the
output LOW.
• Y  AB
• All inputs LOW make the output HIGH.
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Active Logic Levels - NOR
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Logic Switches
• Provides a logic HIGH or LOW
depending on switch position.
• Commonly used types include normallyopen pushbutton, normally-closed
pushbutton, single-pole single-throw,
and single-pole double-throw.
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Logic Switches
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Logic Switches
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Two-Pole Push Button
• Two-pole push button allows for
normally HIGH and normally LOW
levels from the same switch.
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Two-Pole Push Button
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Light Emitting Diodes (LED’s)
• Used to indicate the status of a digital
output.
• Has two terminals the anode and the
cathode.
• If the anode is approximately 1.5 V
greater than the cathode, current flows
and the LED illuminates.
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Light Emitting Diodes (LED’s)
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Light Emitting Diodes (LED’s)
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Light Emitting Diodes
• Used to provide a visual indication of a
logic state.
• Can be wired to display active-HIGH or
active-LOW.
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Light Emitting Diodes
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Light Emitting Diodes
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Logic Gate Enable
• The input to a gate that allows the
output to respond to other inputs.
• A logic LOW for an OR or NOR gate, a
logic HIGH for an AND or NAND gate.
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Logic Gate Inhibit
• The input to a gate that forces the
output to ignore any other input.
• A logic HIGH for an OR or NOR gate, a
logic LOW for an AND or NAND gate.
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Logic Gate Inhibit
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Logic Gate Inhibit
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Logic Gate Inhibit
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Logic Gate Inhibit
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Logic Gate Inhibit
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Logic Gate Inhibit
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Logic Gate Inhibit
Control
AND
OR
NAND
NOR
XOR
XNOR
A=0
Y=0
Y=B
Y=1
Y B
Y=B
Y B
A=1
Y=B
Y=1
Y B
Y=0
Y B
Y=B
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Tristate Buffer
• Three output states, HIGH, LOW and
high-impedance.
• Requires a separate input to control
which output state is selected.
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Tristate Buffer
74
Tristate Buffer
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Tristate Buffer Utilization
• Used to connect multiple outputs
together.
• Used in controlling the operation of
buses.
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Tristate Buffer Utilization
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The 74LS244 Octal Tri-State
Buffer
• Contains two groups of four noninverting tri-state buffers.
• Each group is controlled by a separate
enable input.
G
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The 74LS244 Octal Tri-State
Buffer
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Integrated Circuit Package
• Integrated Circuits (ICs) contain many
components in a single package.
• Several packaging options are
available.
• One common package is called dual-inline (DIP).
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Integrated Circuit Package
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Integrated Circuit Technology
• One common form is transistortransistor logic, called TTL.
• The other common form is
Complementary Metal-Oxide
Semiconductor, called CMOS.
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Integrated Circuit Technology
Part Number
Logic Family
74LS00
Low-power Schottky TTL
74ALS00
Advanced low-power Schottky TTL
74F00
FAST TTL
74HC00
High-speed CMOS
74CT00
High-speed CMOS (TTL-compatible inputs)
74LVX00
74ABT00
Low-voltage CMOS
Advanced BiCMOS (TTL/CMOS hybrid)
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Integrated Circuit Designation
• Standard form is 74XXFF, where 74 is
the logic family identifier, XX is the logic
family member and FF identifies the
specific logic function.
• SN74ALS00N
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IC Package Options
• PLCC - plastic lead chip carrier
• SOIC - small outline integrated circuit
• TSSOP – thin shrink small outline
package
• QFP – quad flat pack
• DIP – dual inline package
• BGA – ball grid array
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IC Package Options
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PLCC 84 Pin Packages
• Can be mounted on the surface of a
circuit board or mounted in a socket.
• Pins are equally distributed on four sides.
• Pin 1 placed on the center of one of the
rows, as indicated by a dot.
• Pins number counterclockwise from this
point.
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PLCC 84 Pin Packages
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