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CHAPTER 2:
DIGITAL ELECTRONICS WITH MULTISIM
edited by: engr noor badariah asan
INTRODUCTIONINTRODUCTION
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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OverviewOverview
Electronics Workbench is used by industry for developing a broad range of products: Power Electronics Communications Consumer Electronics Robotics & Automation Test & Instrumentation Controls Biomedical
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Advantages of MultiSIMAdvantages of MultiSIM
Fast and easy schematic entry. Components are grouped logically by device family for
quick access.
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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.
Advantages of MultiSIMAdvantages of MultiSIM
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Replacing a part with another member of the same device family is fast and simple.
Just double-click on the part and select the replacement.
Wires in EWB “auto-route” so that you can move components around the screen without breaking connections.
Advantages of MultiSIMAdvantages of MultiSIM
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Advantages of MultiSIMAdvantages of MultiSIM
Simulator 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.
High-Quality Model 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 InterfaceMultiSIM Interface
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Basic Elements:Basic Elements:
Multisim’s user interface consists of the following 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.
Basic Elements:Basic Elements:
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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.
The Design Bar guides you through the logical steps of building, simulating, analyzing and, eventually, exporting your design.
Design BarDesign Bar
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Design BarDesign Bar
The Component Design Bar button is selected by default, since the first logical activity is toplace 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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ComponentComponent
sources
basics
diodes
transistors
Analog ICs
Mixed ICs
Digital ICs
Digital Gates
Miscellaneous
controls
Indicators
Latches
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SourcesSources
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
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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Connector Resistor Capacitor Inductor Transformer Relay Switch Time-Delay Switch Voltage-Controlled Switch Current-Controlled Switch Pull-up Resistor
Potentiometer Resistor Pack Voltage-Controlled Analog Switch Polarized Capacitor Variable Capacitor Variable Inductor Coreless Coil Magnetic Core Nonlinear Transformer
BasicsBasics
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DiodesDiodes
Diode Zener Diode LED Full Wave Bridge Rectifier Shockley Diode Silicon Controlled Rectifier Diac Triac
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NPN Transistor PNP Transistor N-Channel JFET P-Channel JFET 3-Terminal Depletion N-MOSFET 3-Terminal Depletion P-MOSFET 4-Terminal Depletion N-MOSFET
4-Terminal Depletion P-MOSFET 3-Terminal Enhanced N-MOSFET 3-Terminal Enhanced P-MOSFET 4-Terminal Enhanced N-MOSFET 4-Terminal Enhanced P-MOSFET N-Channel GaAsFET P-Channel GaAsFET
TransistorTransistor
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Analog and Mixed ICsAnalog 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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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)
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)
Digital ICsDigital 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)
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)
Digital ICsDigital 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))
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)
Digital ICsDigital 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))
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)
Digital ICsDigital ICs
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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
Schmitt Trigger AND Gates OR Gates NAND Gates NOR Gates NOT Gates XOR Gates XNOR Gates
Digital GatesDigital Gates
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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
LatchesLatches
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Voltmeter Ammeter Bulb Probe 7-Segment Display Decoded 7 Segment Display Buzzer Bargraph Display Decoded Bargraph Display
IndicatorsIndicators
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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
ControlsControls
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MiscellaneousMiscellaneous
Fuse Write Data Lossy Transmission Lossless Transmission Crystal DC Motor Triode Vacuum
Boost Converter Buck Converter Buck-Boost Converter Textbox Title Block Netlist Component
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InstrumentsInstruments
Instruments are accessed through the Instruments button on the Design Bar. When you clickthis button, the Instruments toolbar appears. It includes one button for each instrument.
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Oscilloscope Oscilloscope
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.
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Add Instrument
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OscilloscopeOscilloscope
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 AnalyzerLogic Analyzer
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 GeneratorFunction Generator
The Function Generator produces square, triangular and sinusoidal waves.
You can control the frequency, duty cycle, amplitude and DC offset.
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MultimeterMultimeter
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 GeneratorWord Generator
The Word Generator can drive a circuit by producing streams of 16-bit words.
It can be configured to step one word at a time, burst through user-defined sets of data, or cycle continuously at a specified frequency.
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Bode PlotterBode Plotter
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 CIRCUITBUILDING A CIRCUIT
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Drawing a basic schematic circuit
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1.0: Placing Component on Circuit Window1.0: Placing Component on Circuit Window The component toolbar:
Placing your cursor onone 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 Component1.1: Placing the First Component
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.
Step 1: Placing a 5V Battery
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1) To change the battery’s value, Double-click on the battery. The battery’s properties screen appears, with the Value tab displayed.
2) Change the “12” to a “5” and click OK.
Step 2: Change the Battery Value
To save your changes, choose File/Save As, and give a name (and location) for your circuitfile.
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1.2: Placing the Next Components1.2: Placing the Next ComponentsStep 1: Place a Resistor
1) Place your cursor on the Basic Parts Bin button and, from the toolbar that appears, click the Resistor button.
2) The resistor’s Browser screen appears.3) This Browser screen appears because the
Resistor family contains multiple real components that you could actually purchase.
4) Scroll through the Component List to find the 470ohm resistor. Select the 470ohm
resistor and click OK.5) To rotate the resistor, Right-click on the
resistor. A pop-up menu appears. Choose 90CounterCW from the menu.
6) 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) To add the other resistors, add a 120ohm resistor at the intersection.
2) Notice how this second resistor is given the reference ID “R2”, to indicate it is the second resistor placed.
3) 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.
4) 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.
5) To move components to the desired location, simply single-click the component to select it
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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.
1.3: Placing Other Components1.3: Placing Other Components
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1.4: Wiring Component1.4: 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. Click the pin coming out of the bottom of V1.
2. Click the pin on the top of the ground. The two components automatically become wired together.
3. To stop the wiring process, press ESC.
4. To delete a wire, right-click on it and choose Delete from the pop-up menu, or press DELETE.
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To change the label of any individual component you have placed:
1. Double-click on the component. The component’s properties screen appears.
2. Click the Label tab and enter or modify the label (which must be composed of letters or numbers only—no special characters or spaces).
3. 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.
1.5: Changing Label and Color of Individual Components and Nodes
1.5: Changing Label and Color of Individual Components and Nodes
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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. Choose Edit/Place Text.2. Click anywhere on the circuit window. A text box appears.3. Type the text—for example, type “My tutorial circuit”.4. Click on the location on the circuit window where you want the text placed. The mouse
was clicked at these points.5. To delete text, right-click on the text box and choose Delete from the pop-up menu or
press DELETE.6. To change the color of text, right-click on the text box, choose Color from the pop-up
menu, and choose the desired color.7. 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.8. To move text, click on the text box and drag it to a new location.
1.6: Adding Text to the Circuit1.6: Adding Text to the Circuit
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1.6: Adding Instrument to the Circuit1.6: 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 Circuit1.6: 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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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
Analyzing the CircuitAnalyzing 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.
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
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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
V112V 50Hz 0Deg
V212V
X112V_25W
X2
12V_25W 1.463 A
+-
2.069 A+ -
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Digital Waveform
V1 500Hz 5V
U1A
7432N
1
2
3
X1
2.5 V
A BT
G
XSC1
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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
Key = Space
V1
5V
R1
1kOhm
U4
NOT
4.500 V+
- 5.000p V
+
-
1
0
2
3
A Y
0 1
1 0
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INVERTER CIRCUIT USING IC TTL 7404 HEX INVERTER
V1
5V
S1
Key = Space
R1
1kohm
XMM1U1A
7404N
21U1B
7404N
43
U1C
7404N
65U1D
7404N
89U1E
7404N
1011U1F
7404N
1213
X1 X3 X2
X5 X4 X7 X6
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INVERTER CIRCUIT
V1120V Y
A'
R1
100ohm
YCBA
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OR Gate
S1
Key = A
U1A
7432N
1
23
V1
1000Hz 5V
R1
1kOhm
A BT
G
XSC1
High
LowV2
5V
INPUT A
INPUT B
OUTPUT, Y
0 0 0
0 1 1
1 0 1
1 1 1
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R1
1kOhm
V1
5V
S1
Key = B
U2A
7432N
1
23
U2B
7432N
4
56
S2
Key = C
S3
Key = D
U2C
7432N
9
108
S4
Key = A
S6 Key = E
U2D
7432N
12
1311
X1
OR CIRCUIT USING IC TTL 7432
5 INPUT OR GATE
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AND GATE
QC T
1
F
XLA1
A BT
G
XSC1
V1 500Hz 5V
V25V
U1A
74LS08J
1
23
A B Y
0 0 0
0 1 0
1 0 0
1 1 1
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AND GATE USING TTL 7408 IC
R1
1kOhm
S1
Key = A
V1
5V
S2
Key = B
U1A
7408J
1
23
U1B
7408J
4
56
S3 Key = C
U1C
7408J
9
108
U1D
7408J
12
1311
S4 Key = D
S5 Key = E
X1 X2 X3 X4
5 INPUT AND GATE
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AND and OR CIRCUIT
V112V
Y
A B C
AND CIRCUIT
A .B = Y
V112V Y
A
B
C
OR CIRCUIT
A + B = Y
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NAND GATE
A B Y
0 0 1
0 1 1
1 0 1
1 1 0Input B
Input AU1
R1 10kOhm
Output Y
V1
5V
S1
Key = B
S2
Key = A
X1
7400 NAND GATE
Key point for NAND:i) Output for NAND gate invert
output AND gate
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NOR GATE
V1
5V
R1 10kohm
X1
U1A
7428N
2
31
U1B
7428N
5
64
U1C
7428N
8
910
U1D
7428N
11
1213
U3A
7428N
2
31
J1
Key = A
J3
Key = B
J2
Key = C
J5
Key = D
5VVCC
X3
X2
A B Y
0 0 1
0 1 0
1 0 0
1 1 0
4 INPUT NOR GATE USING TTL7428
Key point for NOR:i) Output for NOR gate invert
output OR gate
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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
4030BD
1
2
3
U1A
23
4009BCL
U2A
45
4009BCL
U2B
U3A
4081BD
1
23
U3B
4081BD
5
64
U4A
7432N
1
2
3
AB
Y
A
B
A'
B'
Y
Two-Input XOR Truth Table for A B = Y
A B Y
0 0 0
0 1 1
1 0 1
1 1 0
XOR Truth Table
A B = Y
Key point for XOR:i) Two inputs are same, output = 0ii) Two inputs are different, output = 1
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XOR CIRCUIT USING TTL 7486 IC
R1
1kohmV1
5V
7486N
1
23
U1A
7486N
4
56
U1B
7486N
9
108
U1C
7486N
12
1311
U1D
J1
Key = A
J3
Key = B
X1
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XNOR LOGIC CIRCUIT23
4009BCL
U2A
45
4009BCL
U2B
U3A
4081BD
1
23
U3B
4081BD
5
64
A
B
A'
B'
Y
U5A
74HC02N
2
31
U1
ENOR2
A
BY
Two-Input XNOR Truth Table
A B Y
0 0 1
0 1 0
1 0 0
1 1 1
Table 3-3 XNOR Truth Table
YBA Key point for XNOR:i) Two inputs are same, output = 1ii) Two inputs are different, output = 0
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R1
1kohm
V1
5V
U2
ENOR2
X1
J1
Key = A
J2
Key = B
XNOR CIRCUIT USING 74LS266N
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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
2) A + 1 = 1
3) A . 0 = 0
4) A . 1 = A
5) A + A = A
6) A + A’ = 1
7) A . A = 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.
YXYX YXYX
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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
V1
5V
R1
1kOhm
R2
1kOhm
U1
AND2U2A
7400N
1
23
U2B
7400N
4
56
A
BY2
Y1
X1
X2
J1
Key = A
J2
Key = B
Universal NAND as AND gate
V1
5V
5V
VCC
R1
1kohm
R3
1kohm
S1
Key = AS3
Key = B
U1
AND2U3A
7402N
2
31
U3B
7402N
5
64
U3C
7402N
8
910
AB Y1
Y2
X1
X3
Universal NOR as AND gate
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Example 1: Representing OR gate with 2-input NAND gate.
BAY
BAY
BAY
Figure: Replacing OR gate with NAND gates
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Example 2: Representing AND gate with 2 input NAND gate.
BAY
BAY
Figure: Replacing an AND gate with NAND gates
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Example 3: Representing a NOR gate with 2 input NAND gate.
BAY
BAY
BAY
Figure 2.21: Replacing a NOR gate with AND gate
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1) From a Boolean Expression to a Logic Circuit
Eg: X = AB + C (Boolean expression)
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Implementing Combinational Circuit
Logic circuit
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Implementing Combinational Circuit 2) From a Truth Table to a Logic Circuit
Eg: A 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
Truth Table
Logic circuit?
- Get the Boolean exp:
X = A’BC + AB’C’
- Draw logic circuit
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Answer: X = A’BC + AB’C’ Logic circuit:
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Implementing Combinational Circuit
U1A
7404N
21
U1B7404N
43
U1C7404N
65
1
2
8
9
U2A
4073BD
3
4
5
6
U2B
4073BD
U3A
74HC32N
1
2
3
A
B
C
X
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Combinational Circuit
U1A
7408J
1
23
U1B
7408J
4
56
V1
5V
S1
Key = B
S2
Key = A
U2A
7404N
21
U2B
7404N
43 R1
1kohm
5V
VCC
U3A
7402N
2
31
X1
Determine the Boolean equationfor this circuit.
Ans: Boolean Equation after simplify: (A + B’) . (A’ + B)
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Combinational circuit
V2
5V
S1
Key = A
S2
Key = B
S3
Key = C
U1
AND2
R1
1kOhm
U3
OR2
U4
OR2
U5
AND2
U6
AND2
X1
U2
NOT
U7
NOT
U8
NOT
Construct digital logic circuit for Y=(A+BC’)((AB)’+C)
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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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1)Looping Groups of Two (Pairs)
Eg:
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Looping K-MAP
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Looping K-MAP2)Looping Groups of Four (Quads)
Eg:
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Looping K-MAP3)Looping Groups of Eight (Octets)
Eg:
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MultiSim: Arithmetic Circuits, Flip-flops, Counters, Shift
Registers and Multiplexers