Transcript CHAPTER 2 Week 4

CHAPTER 2:
DIGITAL ELECTRONICS WITH
MULTISIM
INTRODUCTION
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To become familiar with Multisim – A computer program which
simulates analog and digital circuits.
Multisim is a product made by Electronics Workbench (indeed, the
program used to be simply called Electronics Workbench).
The program simulates analog and digital circuits.
In this course, we will only use a few of the features available in
Multisim for digital circuits.
Comes with exceptionally easy to use schematic capture.
Design entry is faster and more convenient.
Components are grouped logically by device family for quick access.
No need to scroll through large library files searching for the part you
need.
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Overview
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Electronics Workbench is used by industry for developing
a broad range of products:
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Power Electronics
Communications
Consumer Electronics
Robotics & Automation
Test & Instrumentation
Controls
Biomedical
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Advantages of MultiSIM
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Fast and easy schematic entry.
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Components are grouped logically by device family for
quick access.
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Advantages of MultiSIM
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Components can be dropped on a wire and Electronics Workbench
automatically makes the connection.
To wire components together, simply drag from one connector to
another connector.
You can route wires manually or turn on the “Auto-route” feature and
the program routes wires for you.
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Advantages of MultiSIM
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Replacing a part with another
member of the same device family
is fast and simple.
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Just double-click on the part and
select the replacement.
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Wires in EWB “auto-route” so that
you can move components around
the screen without breaking
connections.
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Advantages of MultiSIM
Simulator
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High-Quality Model
With EWB, you can change
component values while you
simulate - no need to stop your
simulation, make hangs, and
then re-simulate.
Circuits can be tweaked and
components can be changed
faster and more easily with a
simulator than they can be by
hand calculation or on a lab
bread-board.
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Electronics Workbench comes
with one of the largest
component libraries.
Know exactly how your circuit
behaves before you order
components.
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MultiSIM Interface
Basic Elements:
Multisim’s user interface consists of the following basic elements:
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Basic Elements:
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The system toolbar contains buttons for commonly-performed
functions.
The Multisim Design Bar is an integral part of Multisim.
The “In Use” list lists all the components used in the current
circuit, for easy re-use.
The component toolbars contain Parts Bin buttons that let you
open component family toolbars.
The circuit window is where you build your circuit designs.
The database selector allows you to choose which database
levels are to be visible as component toolbars.
The status line displays useful information about the current
operation and a description of the item the cursor is currently
pointing to.
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Design Bar
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The Design Bar is a central component of Multisim,
allowing you easy access to the sophisticated
functions offered by the program.
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The Design Bar guides you through the logical steps
of building, simulating, analyzing and, eventually,
exporting your design.
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Design Bar
The Component Design Bar button is selected by default, since the first logical activity is to
place components on the circuit window.
The Component Editor Design Bar button lets you modify the components, or add components.
The Instruments Design Bar button lets you attach instruments to your circuit and see the results
of your simulation on those instruments.
The Simulate Design Bar button lets you start, stop or pause the simulation of your circuit design.
The Analysis Design Bar button lets you choose the analysis you want to perform on your circuit.
The Postprocessor Design Bar button lets you perform further operations on the results of your
simulation.
The VHDL/Verilog Design Bar button allows you to work with VHDL modeling (not available in all
versions).
The Reports Design Bar button lets you print reports about your circuits (Bill of Materials, list of
components, component details).
The Transfer Design Bar button lets you communicate with and export to other programs, such as
Ultiboard, also from Electronics Workbench. You can also export simulation results to programs
such as MathCAD and Excel.
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Component
Digital
ICs
Indicators
diodes
Analog
ICs
sources
basics
Mixed
ICs
Digital
Gates
Miscellaneous
controls
Latches
transistors
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Sources
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Ground
Battery
DC Current Source
AC Voltage Source
AC Current Source
Voltage-Controlled Voltage
Source
Voltage-Controlled Current Source
Current Controlled Voltage Source
Current Controlled Current Source
Vcc Source
Vdd Source
Clock
AM Source
FM Source
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Voltage-Controlled Sine Wave
Oscillator
Voltage-Controlled Triangle Wave
Oscillator
Voltage-Controlled Square Wave
Oscillator
Controlled One-Shot
Piecewise Linear Source
Voltage-Controlled Piecewise
Linear
Source
Frequency-Shift-Keying Source
(FSK Source)
Polynomial Source
Nonlinear Dependent Source
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Basics
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Connector
Resistor
Capacitor
Inductor
Transformer
Relay
Switch
Time-Delay Switch
Voltage-Controlled Switch
Current-Controlled Switch
Pull-up Resistor
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Potentiometer
Resistor Pack
Voltage-Controlled
Analog
Switch
Polarized Capacitor
Variable Capacitor
Variable Inductor
Coreless Coil
Magnetic Core
Nonlinear Transformer
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Diodes
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Diode
Zener Diode
LED
Full Wave Bridge Rectifier
Shockley Diode
Silicon Controlled Rectifier
Diac
Triac
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Transistor
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NPN Transistor
PNP Transistor
N-Channel JFET
P-Channel JFET
3-Terminal Depletion NMOSFET
3-Terminal Depletion PMOSFET
4-Terminal Depletion NMOSFET
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4-Terminal Depletion PMOSFET
3-Terminal Enhanced NMOSFET
3-Terminal Enhanced PMOSFET
4-Terminal Enhanced NMOSFET
4-Terminal Enhanced PMOSFET
N-Channel GaAsFET
P-Channel GaAsFET
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Analog and Mixed ICs
Analog ICs:
 3-Terminal Opamp
 5-Terminal Opamp
 7-Terminal Opamp
 9-Terminal Opamp
 Comparator
 Phase-Locked Loop
Mixed ICs:
 A-D Converter
 D-A Converter (I)
 D-A Converter (V)
 Monostable
 555 Timer
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Digital ICs
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4000 (Dual 3-In NOR and INVERTER)
4001 (Quad 2-In NOR)
4002 (Dual 4-In NOR)
4008 (4-bit Binary Full Adder)
4009(Hex INVERTER)
4010(Hex BUFFER)
4011 (Quad 2-In NAND)
4012 (Dual 4-In NAND)
4013 (Dual D-type FF (+edge))
4014 (8-bit Static Shift Reg)
4015 (Dual 4-bit Static Shift Reg)
4017 (5-stage Johnson Counter)
4019 (Quad 2-In MUX)
4023 (Tri 3-In NAND)
4024 (7-stage Binary Counter)
4025 (Tri 3-In NOR)
4027 (Dual JK FF (+edge, pre, clr))
4028 (1-of-10 Dec)
4030 (Quad 2-In XOR )
4040 (12-stage Binary Counter)
4041 (Quad True/Complement BUFFER)
4042 (Quad D-latch)
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4043 (Quad RS latch w/3-state Out)
4044 (Quad RS latch w/3-state Out)
4049 (Hex INVERTER)
4050 (Hex BUFFER)
4066 (Quad Analog Switches)
4068 (8-In NAND)
4069 (Hex INVERTER)
4070 (Quad 2-In XOR)
4071 (Quad 2-In OR)
4072 (Dual 4-In OR)
4073 (Tri 3-In AND)
4075 (Tri 3-In OR)
4076 (Quad D-type Reg w/3-state Out)
4077 (Quad 2-In XNOR)
4078 (8-In NOR)
4081 (Quad 2-In AND)
4082 (Dual 4-In AND)
4085 (Dual 2-Wide 2-In AND-OR-INVERTER)
4086 (4-Wide 2-In AND-OR-INVERTER)
4093 (Quad 2-In NAND (Schmitt))
4502 (Strobe hex INVERTER)
4503 (Tri-state hex BUFFER w/Strobe)
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Digital ICs
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4508 (Dual 4-bit latch)
4510 (BCD up/down Counter)
4511(BCD to Seven-Segment latch/Dec)
4512 (8-In MUX w/3-state Out)
4514 (1-of-16 Dec/DEMUX w/Input latches)
4515 (1-of-16 Dec/DEMUX w/Input latches)
4516 (Binary up/down Counter)
4518 (Dual BCD Counter)
4520 (Dual Binary Counter)
4532 (8-bit priority Enc)
4556 (Dual 1-of-4 Dec/DEMUX)
40106 (Hex INVERTER (Schmitt))
7400 (Quad 2-In NAND)
7402 (Quad 2-In NOR)
7403 (Quad 2-In NAND (LS-OC))
7404 (Hex INVERTER)
7405 (Hex INVERTER (LS-OC))
7406 (Hex INVERTER (HC-OD))
7407 (Hex BUFFER (HC-OD))
7408 (Quad 2-In AND)
7409 (Quad 2-In AND (LS-OC))
7410 (Tri 3-In NAND)
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7411 (Tri 3-In AND)
7412 (Tri 3-In NAND (LS-OC))
7414 (Hex INVERTER (Schmitt))
7416 (Hex INVERTER (HC-OD))
7417 (Hex BUFFER (HC-OD))
7420 (Dual 4-In NAND)
7421 (Dual 4-In AND)
7422 (Dual 4-In NAND (LS-OC))
7425 (Dual 4-In NOR w/Strobe)
7426 (Quad 2-In NAND)
7427 (Tri 3-In NOR)
7428 (Quad 2-In NOR)
7430 (8-In NAND)
7432 (Quad 2-In OR)
7433 (Quad 2-In NOR (LS-OC))
7437 (Quad 2-In NAND)
7439 (Quad 2-In NAND (LS-OC))
7438 (Quad 2-In NAND (LS-OC))
7440 (Dual 4-In NAND)
7442 (4-BCD to 10-Decimal Dec)
7445 (BCD-to-Decimal Dec)
7447 (BCD-to-Seven-Segment Dec)
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Digital ICs
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7451 (AND-OR-INVERTER)
7454 (4-wide AND-OR-INVERTER)
7455 (2-wide 4-In AND-OR-INVERTER)
7469 (Dual 4-bit Binary Counter)
7472 (AND-gated JK MS-SLV FF (pre, clr))
7473 (Dual JK FF (clr))
7474 (Dual D-type FF (pre, clr))
7475 (4-bit Bistable Latches)
7476 (Dual JK FF (pre, clr))
7477 (4-bit Bistable Latches)
7478 (Dual JK FF (pre,com clk&clr))
7486 (Quad 2-In XOR)
7490 (Decade Counter)
7491 (8-bit Shift Reg)
7492 (Divide-by-twelve Counter)
7493 (4-bit Binary Counter)
74107 (Dual JK FF(clr))
74109 (Dual JK' FF(+edge, pre, clr))
74112 (Dual JK FF(-edge, pre, clr))
74113 (Dual JK MS-SLV FF (-edge, pre))
74114 (Dual JK FF (-edge, pre, com clk & clr))
74116 (Dual 4-bit latches (clr))
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74125 (Quad bus BUFFER w/3-state Out)
74126 (Quad bus BUFFER w/3-state Out)
74132 (Quad 2-In NAND (Schmitt))
74133 (13-In NAND)
74134 (12-In NAND w/3-state Out)
74138 (3-to-8 Dec)
74139 (Dual 2-to-4 Dec/DEMUX)
74145 (BCD-to-Decimal Dec)
74147 (10-to-4 Priority Enc)
74148 (8-to-3 Priority Enc)
74150 (1-of-16 Data Sel/MUX)
74151 (1-of-8 Data Sel/MUX)
74153 (Dual 4-to-1 Data Sel/MUX)
74154 (4-to-16 Dec/DEMUX)
74155 (Dual 2-to-4 Dec/DEMUX)
74156 (Dual 2-to-4 Dec/DEMUX (LS-OC))
74157 (Quad 2-to-1 Data Sel/MUX)
74158 (Quad 2-to-1 Data Sel/MUX)
74159 (4-to-16 Dec/DEMUX (LS-OC))
74160 (Sync 4-bit Decade Counter (clr))
74162 (Sync 4-bit Decade Counter)
74163 (Sync 4-bit Binary Counter)
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Digital ICs
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74164 (8-bit Parallel-Out Serial Shift Reg)
74165 (Parallel-load 8-bit Shift Reg)
74166 (Parallel-load 8-bit Shift Reg)
74169 (Sync 4-bit up/down Binary Counter)
74173 (4-bit D-type Reg w/3-state Out)
74174 (Hex D-type FF (clr))
74175 (Quad D-type FF (clr))
74181 (Alu/Function Generator)
74190 (Sync BCD up/down Counter)
74191 (Sync 4-bit up/down Counter)
74192 (Sync BCD up/down Counter)
74194 (4-bit Bidirectional Univ. Shift Reg)
74195 (4-bit Parallel-Access Shift Reg)
74198 (8-bit Shift Reg (shl/shr ctrl))
74199 (8-bit Shift Reg (sh/ld ctrl))
74238 (3-to-8 line Dec/DEMUX)
74240 (Octal BUFFER w/3-state Out)
74241 (Octal BUFFER w/3-state Out)
74244 (Octal BUFFER w/3-state Out)
74251 (Data Sel/MUX w/3-state Out)
74253 (Dual 4-to-1 Data Sel/MUX w/3-state Out)
74257 (Quad 2-to-1 line Data Sel/MUX)
74258 (Quad 2-to-1 line Data Sel/MUX)
74266 (Quad 2-In XNOR (LS-OC))
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74273 (Octal D-type FF)
74279 (Quad SR latches)
74280 (9-bit odd/even parity generator/checker)
74290 (Decade Counter)
74293 (4-bit Binary Counter))
74298 (Quad 2-In MUX)
74350 (4-bit Shifter w/3-state Out)
74352 (Dual 4-to-1 Data Sel/MUX)
74353 (Dual 4-to-1 Data Sel/MUX w/3-state Out)
74365 (Hex Bus Driver w/3-state Out)
74367 (Hex Bus Driver w/3-state Out)
74368 (Hex Bus Driver w/3-state Out)
74373 (Octal D-type Transparent Latches)
74374 (Octal D-type FF (+edge))
74375 (4-bit Bistable Latches)
74377 (Octal D-type FF w/en)
74378 (Hex D-type FF w/en)
74379 (Quad D-type FF w/en)
74393 (Dual 4-bit Binary Counter)
74395 (4-bit Cascadable Shift Reg w/3-state Out)
74445 (BCD-to-Decimal Dec)
74465 (Octal BUFFER w/3-state Out)
74466 (Octal BUFFER w/3-state Out)
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Digital Gates
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2-Input AND Gate
2-Input OR Gate
NOT Gate
2-Input NOR Gate
2-Input NAND Gate
2-Input XOR Gate
2-Input XNOR Gate
Tristate Buffer
Buffers
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Schmitt Trigger
AND Gates
OR Gates
NAND Gates
NOR Gates
NOT Gates
XOR Gates
XNOR Gates
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Latches
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Half Adder
Full Adder
RS Flip-Flop
JK Flip-Flop with Active High Asynchronous Inputs
JK Flip-Flop with Active Low Asynchronous Inputs
D Flip-Flop with Active Low Asynchronous Inputs
Multiplexer ICs
Demultiplexer ICs
Encoder ICs
Arithmetic ICs
Counter ICs
Shift Register ICs
Flip-Flops ICs
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Indicators
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Voltmeter
Ammeter
Bulb
Probe
7-Segment Display
Decoded 7 Segment Display
Buzzer
Bargraph Display
Decoded Bargraph Display
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Controls
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Voltage Differentiator
Voltage Integrator
Voltage Gain Block
Transfer Function Block
Multiplier
Three-Way Voltage Summer
Divider
Voltage Limiter
Voltage-Controlled Limiter
Current Limiter Block
Voltage Hysteresis
Voltage Slew Rate
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Miscellaneous
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Fuse
Write Data
Lossy Transmission
Lossless Transmission
Crystal
DC Motor
Triode Vacuum
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Boost Converter
Buck Converter
Buck-Boost Converter
Textbox
Title Block
Netlist Component
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Instruments
Instruments are accessed through the Instruments button on the Design Bar. When you click
this button, the Instruments toolbar appears. It includes one button for each instrument.
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Oscilloscope
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The dual-trace oscilloscope supports internal or external triggering
on the positive or negative edge.
The time base is adjustable from 0.1ns to 1 s, with a voltage
resolution of 10 uV to 5 kV per division.
Add Instrument
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Oscilloscope
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Colored graphs on the scope correspond to the same colored
connections to the circuit. Note how the display changes as the
scales are altered with the cursor.
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Logic Analyzer
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The Logic Analyzer can be triggered internally or externally on
either the negative or positive edge, or by recognition of a
predefined bit pattern.
It is used for fast data acquisition of logic states and advanced
timing analysis.
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Function Generator
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The Function Generator produces square, triangular and
sinusoidal waves.
You can control the frequency, duty cycle, amplitude and DC
offset.
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Multimeter
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The autoranging multimeter measures AC and DC current and
voltage, resistance, and decibel loss.
The internal resistance and current can be easily defined.
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Word Generator
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The Word Generator can drive a circuit by producing streams of 16bit words.
It can be configured to step one word at a time, burst through userdefined sets of data, or cycle continuously at a specified
frequency.
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Bode Plotter
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The bode plotter produces a graph of a circuit’s phase or gain with
respect to frequency.
Useful for analyzing frequency response for all types of circuits.
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BUILDING A CIRCUIT
Drawing a basic schematic circuit
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1.0: Placing Component on Circuit
Window
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The component toolbar:
Placing your cursor on
one of these Parts Bin buttons
displays another toolbar, the
component family toolbar,
containing buttons
representing the component
families contained in that
Parts Bin.
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1.1: Placing the First Component
Step 1: Placing a 5V Battery
1) Place the cursor on the Sources
Parts Bin button (or click it).
2) The contents of the Sources
family toolbar appear.
3) Click the DC Voltage Source
button.
4) Move to the circuit window, where
we want to place the battery.
5) Click in this general area or, use
the page borders as a guide and
click in the intersection of row A
and column 1. The battery appears
on your circuit window.
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Step 2: Change the Battery Value
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2)
To change the battery’s value,
Double-click on the battery. The
battery’s properties screen
appears, with the Value tab
displayed.
Change the “12” to a “5” and
click OK.
To save your changes, choose File/Save As, and give a name (and location) for your circuit
file.
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1.2: Placing the Next Components
Step 1: Place a Resistor
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6)
Place your cursor on the Basic Parts Bin
button and, from the toolbar that appears,
click the Resistor button.
The resistor’s Browser screen appears.
This Browser screen appears because the
Resistor family contains multiple real
components that you could actually purchase.
Scroll through the Component List to find
the 470ohm resistor. Select the 470ohm
resistor and click OK.
To rotate the resistor, Right-click on the
resistor. A pop-up menu appears. Choose
90CounterCW from the menu.
You can move the labels that accompany a
component’s symbol. In particular, you may
want to do this after some rotations, if the
labels are displayed other than as you prefer.
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Step 3: Add Other Resistors
1)
2)
3)
4)
5)
edited by: engr noor badariah asan
To add the other resistors, add a
120ohm resistor at the intersection.
Notice how this second resistor is
given the reference ID “R2”, to
indicate it is the second resistor
placed.
Place the third resistor, a 470ohm
(you could use the “In Use” list for
this if you wish), at roughly the
intersection in window, and rotate it.
At the “In Use” list, just to the right
of the Design Bar. It lists all the
components you have placed so
far. You can easily re-use a
component from this list by clicking
on it.
To move components to the desired
location, simply single-click the
component to select it
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1.3: Placing Other Components



The process of placing other components and creating a
circuit diagram consists of selecting and dragging the
components from a parts bin and connecting the components
using wire.
For example, LED is from the diodes family, BJT_NPN is from
the Transistor group, capacitor is from the basic group, a
ground is from the sources group, and VCC is also from the
sources group.
For a quick way to move components into line, select them
and use the arrow keys on your keyboard to move the
components in grid increments. Lining them up will make
wiring easier.
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1.4: Wiring Component


In MultiSIM, you can choose to
wire components either
automatically or manually.
Automatic wiring avoids wiring
through other components or
overlapping wires. Manual
wiring means you control the
path of the wire on the circuit
window.
To start the wiring process:

1.
2.
3.
4.
Click the pin coming out of the
bottom of V1.
Click the pin on the top of the
ground. The two components
automatically become wired
together.
To stop the wiring process,
press ESC.
To delete a wire, right-click on it
and choose Delete from the
pop-up menu, or press
DELETE.
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1.5: Changing Label and Color of
Individual Components and Nodes
To change the label of any individual component you have
placed:

1.
2.
3.

Double-click on the component. The component’s
properties screen appears.
Click the Label tab and enter or modify the label (which
must be composed of letters or numbers only—no special
characters or spaces).
To cancel changes, click Cancel. To save click OK.
To change the color of any individual component, right-click
on it and choose Color from the pop-up menu. Choose the
desired color from the screen that appears.
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1.6: Adding Text to the Circuit


To add a title block, choose Edit/Set Title Block. Enter the desired title block text in
the field and click OK. The title block appears at the bottom right of the circuit
window.
To add text:
1.
2.
3.
4.
5.
6.
7.
8.
Choose Edit/Place Text.
Click anywhere on the circuit window. A text box appears.
Type the text—for example, type “My tutorial circuit”.
Click on the location on the circuit window where you want the text placed. The mouse
was clicked at these points.
To delete text, right-click on the text box and choose Delete from the pop-up menu or
press DELETE.
To change the color of text, right-click on the text box, choose Color from the pop-up
menu, and choose the desired color.
To edit text, double-click on the text box and make your changes. Click any location out
of the text box to stop editing text.
To move text, click on the text box and drag it to a new location.
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1.6: Adding Instrument to the Circuit


To add instruments, Click the
Instruments button in the
Design Bar. The Instruments
toolbar appears.
Click the desired instruments
(e.x: oscilloscope), the desired
instrument icon will appears in
the circuit window and we need
to wire the instrument with a
correct terminal into the circuit.
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1.6: Simulating the Circuit

To simulate the circuit, click the Simulate button in
the Design Bar. From the pop-up menu, choose
Run/Stop.

To stop the simulation, click the Simulate Design
Bar button. From the pop-up menu, choose
Run/Stop again.
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Analyzing the Circuit
Analysis functions in MultiSIM lets user investigate the circuit. Enable the user to
understand circuit behavior and optimizing or correcting the circuit’s functionality.







DC Operating Point
Transient
AC Frequency Sweep
Fourier
Noise
Distortion
Temperature Sweep







Parameter Sweep
AC & DC Sensitivity
Pole-Zero
Transfer Function
DC Sweep
Worst Case
Monte Carlo
To initiate the analysis, click the Analysis button from the Design Bar and choose the
desired analysis from the pop-up menu.
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Digital Electronics with
MultiSIM
Introduction to Digital Concepts
Concept of digital circuit

In electronics world there are 2 types of
circuit:




Analog circuit
Digital circuit
Digital circuits referred to circuits that deal
only in highs and lows with discrete binary
values.
DIGITAL – only ‘0’ and ‘1’.
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Analog and Digital Circuit
X1
+
2.069
12V _25W
A
X2
V2
-
12V
1.463
V1
+
A
12V _25W
12V 50Hz 0Deg
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Digital Waveform
X1
X SC1
2.5 V
G
U1A
1
3
A
B
T
2
7432N
V1
500Hz 5V
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Boolean Algebra – AND, OR, and NOT
Function




Boolean Algebra has become the preferred method of specifying
the logic or digital circuits.
All logic functions, no matter how complex, that are required in
digital logic can be created from three basic logic functions: AND,
OR and NOT.
The Boolean Algebra variables are the logic inputs to the logic
gates and functions or of even more complex logic circuits.
The more complex gates, such as NAND or NOR can be thought
of as at the bottom level as various combinations of AND, OR
and NOT gates.
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Logic Gates and Combinational Circuits

Basic logic gates:






Inverter or NOT gate
OR gate
AND gate
NAND gate
NOR gate
Advanced Logic Gate:


XOR
XNOR
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INVERTER/NOT GATE
S1
U4
2
Key = S pace
NOT
A
Y
0
1
1
0
3
1
+
+
5.000p
V1
5V
-
V
4.500
R1
V
-
1kOhm
0
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INVERTER CIRCUIT USING IC TTL
7404 HEX INVERTER
X1
X3
X2
S1
1
Key = S pace
U1A
X MM1
U1B
3
2
4
7404N
7404N
V1
5V
X5
5
U1C
6
7404N
X4
9
X7
U1D
11
8
7404N
U1E
10
7404N
X6
13
U1F
12
7404N
R1
1kohm
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INVERTER CIRCUIT
R1
100ohm
V1
120V
A'
Y
A B C Y
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OR Gate
X SC1
G
A
H igh
V2
5V
S1
1
Low
B
T
Key = A
INPUT
A
INPUT
B
OUTPUT,
Y
0
0
0
0
1
1
1
0
1
1
1
1
U1A
3
2
7432N
V1
1000Hz 5V
R1
1kOhm
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OR CIRCUIT USING IC TTL 7432
1
U2A
3
2
7432N
Key = A
S4
4
U2B
6
5
X1
7432N
9
U2C
8
10
Key = B
7432N
S1
12
Key = C
U2D
11
13
S2
7432N
V1
5V
Key = D
S3
R1
S6
Key = E
1kOhm
5 INPUT OR GATE
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AND GATE
X SC1
G
A
B
T
A
B
Y
0
0
0
0
1
0
1
0
0
1
1
1
U1A
1
V2
2
5V
74LS 08J
3
X LA1
1
V1
500Hz 5V
F
C Q
T
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AND GATE USING TTL 7408 IC
X1
1
U1A
3
2
S1
4
X3
U1B
6
5
7408J
Key = A
X2
U1C
9
8
10
7408J
Key = B
X4
12
U1D
11
13
7408J
7408J
S2
S3
Key = C
S4
V1
Key = D
S5
Key = E
R1
5V
1kOhm
5 INPUT AND GATE
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AND and OR CIRCUIT
OR CIRCUIT
AND CIRCUIT
A
A
B
C
B
V1
12V
C
Y
V1
12V
A .B = Y
Y
A+B=Y
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NAND GATE
X1
Key = A
I nput A
U1
Output Y
S2
I nput B
A
B
Y
0
0
1
0
1
1
1
0
1
1
1
0
Key = B
V1
S1
R1
10kOhm
Key point for NAND:
i) Output for NAND gate invert
output AND gate
5V
7400 NAND GATE
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NOR GATE
A
B
Y
0
0
1
0
1
0
1
0
0
1
1
0
X3
J1
U1A
Key = A
2
U1C
1
8
10
3
9
J3
7428N
X1
7428N
U3A
Key = B
2
X2
Key point for NOR:
i) Output for NOR gate invert
output OR gate
1
3
J2
7428N
U1B
Key = C
5
U1D
4
11
13
6
12
J5
7428N
7428N
R1
10kohm
Key = D
V1
5V
VCC
4 INPUT NOR GATE USING TTL7428
5V
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ADVANCED LOGIC CIRCUIT


The Exclusive-OR
(XOR) gate
The Exclusive-NOR
(XNOR) gate

Inside the integrated
circuits, these two exclusive
gates consist of various
combinations of the basic
logic gates that are
necessary to perform the
required tasks.
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XOR LOGIC CIRCUIT
U2A
A
B
U3A
A'
1
3
2
U1A
A
2
3
U4A
4009BCL
1
4081BD
3
2
U3B
Y
2
1
U2B
4030BD
5
B
5
4
4009BCL
4
3
Y
7432N
6
4081BD
B'
Two-Input XOR Truth Table for A  B = Y
A
B
Y
0
0
0
0
1
1
1
0
1
1
1
0
AB=Y
Key point for XOR:
i) Two inputs are same, output = 0
ii) Two inputs are different, output = 1
XOR Truth Table
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XOR CIRCUIT USING TTL 7486 IC
X1
J1
Key = A
1
U1A
3
2
7486N
J3
4
5
Key = B
7486N
R1
V1
U1B
6
1kohm
5V
9
U1C
8
10
7486N
12
U1D
11
13
7486N
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XNOR LOGIC CIRCUIT
U2A
2
3
A
A'
U3A
1
3
2
A
2
4081BD
Y
B
U5A
4009BCL
U1
3
U3B
U2B
E NOR2
5
B
5
4
4009BCL
4
1
Y
74HC02N
6
B'
4081BD
A B  Y
Two-Input XNOR Truth Table
A
B
Y
0
0
1
0
1
0
1
0
0
1
1
1
Key point for XNOR:
i) Two inputs are same, output = 1
ii) Two inputs are different, output = 0
Table 3-3 XNOR Truth Table
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XNOR CIRCUIT USING 74LS266N
X1
J1
U2
Key = A
E NOR2
J2
Key = B
R1
1kohm
V1
5V
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Rules of Boolean Algebra
Boolean
algebra
for
expressing
the
relationship between a logic circuit’s inputs
and outputs.
1) A + 0 = A
5) A + A = A
2) A + 1 = 1
6) A + A’ = 1
3) A . 0 = 0
7) A . A = A
4) A . 1 = A
8) A . A’ = 0
9) A’’ = A
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Demorgan’s Theorem


Demorgan’s theorm gives a procedure for
complementing a complex function.
This theorem indicates and interesting
relationship between NOR, OR, NAND and
AND.
X  Y  X Y
X Y  X  Y
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UNIVERSAL NAND GATE
NAND gates can be used to implement NOT, AND & OR gates.
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UNIVERSAL NOR GATE
NOR gates can be used to implement NOT, AND & OR gates.
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UNIVERSAL GATE NAND AND NOR
X1
X1
J1
U1
A
J2
Key = B
B
4
7400N
2
AND2
U3A
6
7402N
Y2
8
9
V1
7400N
5
U3B
4
6
V1
X3
1
3
U2B
5
Y1
S3
Key = B
3
2
Key = A
X2
AND2
U2A
B
S1
Y1
Key = A
1
U1
A
R1
R2
1kOhm
1kOhm
7402N
5V
U3C
10
Y2
7402N
R1
R3
1kohm
1kohm
5V
VCC
5V
Universal NAND as AND gate
Universal NOR as AND gate
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Example 1: Representing OR gate with 2input NAND gate.
Y  A B
Y  A B
Y  A B
Figure: Replacing OR gate with NAND gates
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Example 2: Representing AND gate with 2
input NAND gate.
Y  A B
Y  A B
Figure: Replacing an AND gate with NAND gates
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Example 3: Representing a NOR gate with 2
input NAND gate.
Y  A B
Y  A B
Y  A B
Figure 2.21: Replacing a NOR gate with AND gate
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Implementing Combinational Circuit

1) From a Boolean Expression to a Logic
Circuit
Eg: X = AB + C (Boolean expression)
Logic circuit
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Implementing Combinational Circuit

2) From a Truth Table to a Logic Circuit
A Eg:
B
C
Output, X Product
Term
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
A’BC
1
0
0
1
AB’C’
1
0
1
0
1
1
0
0
1
1
1
0
Logic circuit?
-Get the Boolean
exp:
X = A’BC + AB’C’
-Draw logic circuit
Truth Table
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Implementing Combinational Circuit


Answer: X = A’BC + AB’C’
Logic circuit:
U1A
2
1
A
U2A
1
7404N
B
9
2
8
4073B D
C
U3A
1
2
3
X
74H C32N
U2B
3
3
4
6
4
5
7404N U1B
5
7404N
4073B D
6
U1C
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Combinational Circuit
1
U2A
2
1
U1A
S2
X1
3
2
7404N
7408J
2
V1
5V
U3A
1
3
Key = A
7402N
S1
3
U2B
4
4
U1B
R1
6
5
1kohm
7404N
Key = B
7408J
Determine the Boolean equation
for this circuit.
V CC
5V
Ans: Boolean Equation after simplify:
(A + B’) . (A’ + B)
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Combinational circuit
Construct digital logic circuit for Y=(A+BC’)((AB)’+C)
V2
S1
U3
U5
X1
Key = A
OR2
5V
AND2
S2
U1
U4
U6
Key = B
OR2
AND2
AND2
R1
S3
1kOhm
Key = C
U2
NOT
U7
NOT
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U8
NOT
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Comparators



A comparator is a digital
hardware electronic device
that compares two numbers
in binary form.
Output a 1 or a 0 at its
output depending on
whether they are the same
or not.
Operation of a single bit
comparator can be
expressed as a truth table
Inputs
Outputs
A
B
A<B
A=B
A>B
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
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KARNAUGH MAP

Karnaugh Map provide a systematic method
for simplifying Boolean expressions.

Also called a K map.

What is Karnaugh map method?
A graphical method of simplifying logic
equations or truth tables.
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Looping K-MAP
1)Looping Groups of Two (Pairs)
Eg:
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Looping K-MAP
2)Looping Groups of Four (Quads)
Eg:
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Looping K-MAP
3)Looping Groups of Eight (Octets)
Eg:
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MultiSim: Arithmetic Circuits, Flip-flops,
Counters, Shift Registers and Multiplexers