logic functions and gates - cc.ntut.edu.tljkau/course/982/dd/chapter02.pdfdesignation. •...
TRANSCRIPT
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Chapter 2
Logic Functions and Gates
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Basic Logic Functions
The three basic logic functions are: AND OR NOT
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Logic Function Representation
Logic functions can be represented:algebraicallyusing truth tablesusing electronic circuits.
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Algebraic Representation
Uses Boolean algebra. Boolean variables have two states
(binary). Boolean operatorsinclude
AND, OR, and NOT.
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Truth Table Representation
Defines the output of a function for every possible combination of inputs.
A system with n inputs has 2n possible combinations.
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Electronic Circuit Representation
Uses logic gates to perform Boolean algebraic functions.
Gates can be represented by schematic symbols.
Symbols can be either distinctive-shapeor rectangular-outline.
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Distinctive Shape Schematic Symbols
Uses different graphic representations for different logic functionsAND, OR, NOT.
Uses a bubble (a small circle) to indicate a logical inversion.
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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.
AY =
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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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111001010000YBA
AND Function
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AND Boolean Representation
AND symbol is or nothing at all.
ABYB AY
==
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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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0110000101010011
1
000A
111
001010000YCB
AND Function Electronic Circuit
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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
111
101
110
000
YBA
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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
011
101
110
100
YBA
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NAND Boolean Representation
Uses AND with an inversion overbar.
BAY =
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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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011
001
010
100YBA
NOR Function
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NOR Boolean Representation
Uses OR with an inversion overbar.
BA Y +=
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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 FunctionTruth Tables
3 Input NAND:
3 Input NOR:
CBA Y =
C B A Y ++=
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01111111
0110000101010011
1
000A
011
001010100
CB C B A ++CBA
3 Input NOR and NAND FunctionTruth Tables
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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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011
101
110
000
YBA
Exclusive OR Gate
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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, i.e., the two inputs are different.
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Exclusive NOR Gate
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111
001
010
100YBA
Exclusive NOR Gate
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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
A
B
C
D
U1A
14011
1
23
U2A
14011
1
23
U3A
14011
1
23
Y
B
A
C
D
U4A
14071
1
23
U6A
14081
1
23
U7A
14081
1
23
Y
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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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C
D
A
B U8A
14001
1
23
U9A
14001
1
23
U10A
14001
1
23
Y
C
D
B
A
U11A
14071
1
23
U12A
14071
1
23
U13A
14081
1
23 Y
Gate Equivalence NOR
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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.
B
A
/B
/A
B
/A
A
/B
U14A
14011
1
23
U15A
14071
1
23
U18A
14001
1
23
U19A
14081
1
23
Y
Y
Y
Y
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DeMorgans Theorem - 1
Break the line and change the sign
B A BA +=B A BA =+
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DeMorgans Theorem - 2
The following are two common errors associated with DeMorgans Theorem:
B A BA ++
B A BA
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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
At least one input HIGH makes the
output LOW. All inputs LOW make the output HIGH.
BA Y +=
BA Y =
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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 normally-open pushbutton, normally-closed pushbutton, single-pole single-throw, and single-pole double-throw.
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Logic Switches
Open=>1Close=>0
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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 (LEDs)
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 (LEDs)
A C/K
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Light Emitting Diodes (LEDs)
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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.
Whats the common rated current flow through the diode? About 10mA
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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.
Somewhat like a controlled switch.
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VCC
VCCJump
CarrierDout Q11384
CB
E
D1
JP4HEADER 2
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C3102/100V
R25
470
R224.7
U5B
4011
5
64
U5A
4011
1
23
R24SVR10K
13
2
R2610K
R212K
R231M
Control Input
DIP14 DIP14May be replaced by 3904.E B C1 2 3
Logic Gate Enable
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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 InhibitNote: P.51 Textbook Error; Forgot to add a inverter in the output terminal
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Logic Gate Inhibit
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Logic Gate Inhibit
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Y = 1
Y = B
OR
Y = 1
NAND
Y = 0
NOR
Y = B
XOR
A = 1
A = 0
Control
Y = BY = B
Y = 0
XNORAND
BY =
BY =BY =
B Y =
Logic Gate Inhibit
NAND, NOR, XNORAND, OR, NOR
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75
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
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Tristate Buffer
Active Low!
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Tristate Buffer Utilization
Used to connect multiple outputs togetherAn action that requires highly attention!.
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 non-inverting tri-state buffers.
Each group is controlled by a separate enable input, i.e., .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-in-
line (DIP).
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Integrated Circuit Package
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Integrated Circuit Technology
One common form is transistor-transistor logic, called TTL.
The other common form is Complementary Metal-Oxide Semiconductor, called CMOS.
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Low-voltage CMOS74LVX00
Advanced low-power Schottky TTL74ALS00FAST TTL74F00
Advanced BiCMOS (TTL/CMOS hybrid)74ABT00
High-speed CMOS (TTL-compatible inputs)74CT00High-speed CMOS74HC00
Low-power Schottky TTL74LS00Logic FamilyPart Number
Integrated Circuit Technology
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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
SOICTSSOP
PLCC
DIP BGA
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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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