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Digital Electronics

Josiah Smith



Course Introduction

This course is rigorous and nationally accredited. Digital Electronics studies electrical circuits that manipulate digital signals. Digital signals are very different than analog signals in that digital signals have two discreet voltages or logic levels. Almost any device today uses digital signals to process information. This course will explore sequential logic, engineering standards, and combinational logic. Students will work with electrical circuits, and will utilize their interpersonal skills, creative abilities and their prior knowledge of the engineering design process.



Personal PageMy name is Josiah Smith. I currently

attend Parkland High school as a junior. I am very active in the Boy Scout program and also with my church youth group. I also enjoy playing my trumpet. I am involved in the school concert band, jazz ensemble, pit orchestra and marching band as well. I have been enrolled in the Project Lead the Way course since freshman year. I have taken both Intro to Engineering Design as well as Principles of Engineering. I also took a class sponsored by my school entitled Innovation and Invention. Another class I participated in was sponsored by Air Products called Explorer Post. I have also earned both the electronics and electricity merit badge in boy scouts.



Unit 1: Digital and Analog Fundamentals

Unit 1 is focused on the basics of electrical engineering and design. Students will learn about components of circuits as well as how to interpret measurements in a circuit. They will also learn the basic measurements used in circuits as well. Students will also learn about data sheets, schematics, transistor-transistor logic and combinational logic gates.1.1 Foundations and the Board Game Counter

1.2 Introduction to Analog

1.3 Introduction to Digital



1.1 Foundations and the Board Game Counter

In this lesson, students will learn the basics of combinational and sequential logic by assembling and analyzing the Game Board Counter. This is a game that emulates a die. Students will also learn safety, scientific and engineering notation, component identification, and proper soldering techniques.

General Safety

Engineers Notation

Electronic Components

Soldering

Game Board Counter



General Safety

The First order of business in section 1.1 is safety. Electronics has many risks associated with it including: Electrocution, burns, chemical damage, and even simple wounds from components. We also learned what causes the danger like increased current, hot soldering irons, sharp components, smoke from soldering or melting, and more. We learned how to prevent these by using simple rules such as avoiding baggy clothing or jewelry, avoiding damp areas, and wear safety goggles!



Engineers Notation

Engineer’s notation is used to shorten long numbers with many digits. For example, would you rather write .000001 seconds or 1 microsecond? One thing to keep in mind is that the engineer’s notation only uses powers of three to shorten numbers. So in the previous example:.000001 = 1 x 10 = 1 microsecond The prefixes used are shown in the table to the right.

-6



Electronic ComponentsIn this section, we learned how to identify all types of electronic components such as resistors, capacitors, LEDs, Integrated Circuits, and more. We also learned how to read the value of resistors and capacitors. Most resistors have a series of colored bands that help a user determine its resistance. There are many types of capacitors which all have different methods of reading the capacitance. We also learned how to measure values with a multimeter.

Electrolytic Capacitors

Multimeter Resistor Color Code



SolderingSoldering uses a tin and lead mixture to melt and adhere to a printed circuit board (PCB)as well as an electronic component by heating the solder to 361° F using a soldering iron. We learned how to solder using correct techniques such as tinning. We also learn the most common mistakes of soldering such as: Too much solder, too little solder, solder bridge or a lifted trace pad. We also learned how to safety handle a soldering iron before testing out soldering on some testing components.



Game Board CounterThe Game Board Counter is a simply electronic die that uses 7 LEDs to display the value of each roll. In this circuit, there is an analog section, a sequential logic section, a combinational logic section , and the LEDs. This circuit also includes a switch, a button, 7 LEDs, 10 resistors, 3 capacitors, 6 Integrated circuits (ICs), 6 IC sockets, and one battery pack.



1.2 Introduction to AnalogThis section will teach students basic circuit theory,

circuit simulation , breadboarding, digital and analog signals. Students will also learn how the game board counter works by using simulation.

Electron Theory

Voltage, Current, and Resistance

Series and Parallel Circuits

Digital and Analog Signals

Measuring Digital Signals

555 Timer

Breadboarding



Electron TheoryElectricity is the flow of electrons. An element is determined by the amount of electrons in an atom’s outermost shell or its valence electrons. The lower the valence electrons, the more conductive an element is because those few valence electrons can more easily be moved into a flow. Generally elements with valence electrons of 1-2 are conductors, 3-6 are semi-conductors, and 7-8 are insulators.



Voltage, Current, and Resistance

Voltage is the electrical force that causes current to flow in a circuit. This is measured in volts. Current is the flow of electrical charge through an electronic circuit. The direction of a current is opposite to electron flow. Current is measured in amperes (amps). Resistance is a measure of opposition to current flow. It is measured in Ohms. Ohm’s law defines the relationship between these three measurements and is defined as V=I x R or voltage = current x resistance.



Parallel and Series Circuits

Series Circuit

Parallel Circuit

There are two different types of circuits. In a series circuit, components are connected end-to-end and there is only one path for current to flow. In a series circuit, the current through every component is equal and the resistances of each component add to equal the total resistance. The sum of the voltages equals the total voltage in a series circuit which is called Kirchhoff’s Voltage Law. In a parallel circuit, both end of components are connected together and there are multiple paths for current to flow. The voltage across every component is equal and the total resistance is equal to the reciprocal of the sum of the reciprocal of the resistance at each component. The sum of the current is equal to total current which is called Kirchhoff’s current law.



BreadboardingA breadboard is a reusable platform for temporarily built electronic circuits. A breadboard is used by putting the leads of electronic components into the holes that are arranged in a grid pattern. A series of metal strips connect rows of holes. Breadboarding is helpful because it takes less time and money and also allows designers to see how the circuit functions and adjust the circuit easily if changes need to be made.



Analog and Digital SignalsThere are two types of electrical signals. One is analog and the other is digital. Analog signals are continuous, have an infinite range of values, and have more exact values. Digital signals are discrete, have a finite range of values, are less exact than analog, and are easier to work with. Digital signals also have a logic high and a logic low. Logic high is generally 5v and logic low is generally 0v. There is a level in between that is an invalid logic level that has no meaning.

Analog Signal

Digital Signal



Measuring Digital SignalsThere are different parts of a digital signal. The Amplitude for digital signals is always 5V. The period is the time it take s for a periodic signal to repeat. The frequency is the number of cycles per second. The time high is the time the signal is high or at 5V. The Time low is the time the signal is low or at 0V. The Duty Cycle is the percent of the period that is Time High. The Rising edge is the 0-to-1 transition of the signal. The falling edge is a 1-to-0 transition of the signal. Digital signals can be measured by using an oscilloscope. Digital Signal



555 TimerA 555 timer is an 8-pin IC that is capable of producing time delays or oscillators. There is basically a general circuit that all 555 timers use. The components that affect the 555 timer are two resistors (Ra and Rb) as well as a capacitor. There are formulas to calculate the period, frequency and duty cycle of a 555 timer output.



1.3 Introduction to Digital

In this lesson, students will learn the basics of combinational and sequential logic as well as further examining and

analyzing the Game Board Counter through simulation. Students will also further be introduced to IC and

datasheets.

Combinational Logic

Sequential LogicIntegrated Circuits

IC DatasheetsGame Board Counter



Combinational LogicCombinational logic has one or more inputs and one or more outputs. The outputs are determined by the inputs at that moment. Combinational logic uses AOI logic. AOI stands for And, Or, and Invert. An AND gate is a gate that requires all true inputs to output true. An OR requires one true input to output true. An INVERTER gate outputs the opposite of the input. All logic gates have truth tables that define all the possible inputs and outputs of a gate.

OR gate truth table

Combinational Logic Schematic



Sequential LogicSequential Logic has one or more inputs and one or more outputs just like combinational logic. The difference is that in sequential logic, the output is affected by the current inputs as well as past inputs. Sequential Logic also utilizes memory or flip-flops and clocks. Sequential logic uses these flip flops in conjunction with each other to create circuits such as a binary counter or the game board counter.

Flip flop used in Game Board Counter



Game Board CounterIn the game board counter, the first section is an Analog section that produces square waves that decrease in frequency and eventually stop. That signal is sent to the Sequential Logic Section which goes through a binary count of 1 to 6 on every clock pulse then repeats. Those signals are then sent to the combinational logic which encodes the binary count into the die’s seven dots.

Illustrative depiction of game board counter



Integrated Circuits

All logic gates are built into Integrated Circuits (ICs). There two main types of technology for circuits: transistor-transistor logic (TTL) which is faster but less energy efficient and Complementary Metal Oxide Semiconductor (CMOS) which uses less power and is slower. There are also many types of integrations which are the amount of gates per IC. There are two main two main types of package styles as well. They are Through-Hole Technology (THT) which is only used for student use today and Surface Mount Technology (SMT) which is used in almost all electronics because of its smaller size.

THT IC

SMT IC



IC Datasheets

IC Datasheets are information sheets containing the general description and function, schematic, function table, recommended operating conditions, electrical characteristics, switching characteristics, and physical dimensions of an IC. These are sometimes included with the IC and other times are found online.



Unit 2: Combination LogicUnit 2 delves deeper into the Combinational Logic aspect of digital electronics. Students will use concepts from Unit 1 and the new concepts of Unit 2 to create various design projects. Required for these projects include the use of truth tables, logic expressions, Boolean Algebra, and Karnaugh mapping to implement AOI, NOR, and NAND logic circuits. These circuits will be demonstrated through physical breadboarding, computer design software, and the Programmable Logic Device (FLD). Students also will learn the basics of XOR, XNOR, and binary adder components. Binary, Octal, and Hexadecimal number systems will also be utilized in this unit.

2.1 Introduction to AOI Logic

2.2 Introduction to NAND/NOR Logic

2.3 Date of Birth Project

2.4 Specific Combinational Logic Circuits & Misc.

2.5 Programmable Logic: Combinational



2.1 Introduction to Combinational Logic

Unit 2.1 highlights the combinational logic portion of digital electronics. Students will build upon their knowledge and learn new techniques and concept which will build up to the Majority Vote project including truth tables, AOI Logic, and simplification methods. Students will also learn about the Computer Design Software and utilize it.

Binary Numbers & Conversions AOL Implementation & Analysis

Truth Tables & Logic Expressions Boolean Algebra & DeMorgan’s Theorems

Majority Vote ProjectAOI Logic



Binary Numbers & ConversionsHumans understand and utilize the decimal or base 10 number system. In this system, each digit represents a multiple of ten. Computers and machines understand the binary or base 2 number system. In this system, every digit represents a multiple of 2. Converting between the two is essential to learn.

Converting from Binary to Decimal System

Conversion from Decimal to Binary System



Truth Tables & Logic ExpressionsTruth Tables display all possible inputs and their corresponding the outputs to show the function of a certain gate. The amount of outputs is proportional to the number of inputs. There are 2^x outputs where x is the number of inputs. From this truth table, a logic expression can be derived. A logic expression shows all sets of inputs that will display a positive, “1”, output.



AOI LogicAOI Logic stand for AND, OR, and Inverter logic. This takes the truth table and logic expressions and creates working circuits from them. There are these various gates used in this form of circuitry. They output either positive or negative based on whether or not the inputs fit the criteria. For example, an AND gate will only output positive when all inputs are positive. An OR gate will output positive when at least one input is positive. An Inverter will output the opposite of the input.

AND Gate

Inverter Gate

OR Gate



AOI Implementation & Analysis

There are two forms of AOI Logic, Sum of Products, and Product of Sums. One or the other is generally used based upon the efficiency. It is important to be able to convert between a logic expression and a circuit. This is discussed in this section. Essentially, if there is a “+” sign in the logic expression, it corresponds with an OR gate and if there is a “x” sign , it corresponds with an AND gate. If a term is, not-ed, an Inverter gate is used.

B A D C B D C B A F2

Example of an implemented logic expression

Example of Analysis of Logic Circuit



Boolean Algebra & DeMorgan’s Theorems

Often times, when a logic expression is taken from a truth table it can be simplified to create a smaller, more efficient. Boolean Algebra is a algebraic method to shorten expressions using the Theorems shown. DeMorgan added to these making more simplification possible.



Majority VoteProblem Statement: A system must be designed to eliminate the unreliable paper ballots that resulted in an unacceptable amount of over-votes and under-votes. This system must record the outcome based on the votes of 4 members.

This project culminated most of the lessons taught in this unit. First, a truth table was derived from the constraints and design statement. Then, a logic expression was derived. This was left un-simplified and was made into a circuit drawing and then a CDS circuit and was tested. Students then returned to the logic expression and simplified it using Boolean Algebra and built a CDs circuit based on that. The two circuits were then compared to show how useful simplification really is.



2.2 Introduction to NAND/NOR Logic

Karnaugh Mapping NAND/NOR Gates Fireplace Project

This Unit expands upon unit 2.1 and adds efficiency to the design process as well as the production faze by keeping costs down. K-Mapping increases efficiency when simplifying logic expressions . The new gates cut down the amount of ICs needed. The Fireplace project culminated unit 2.1 and 2.2 and also requires breadboarding for the final circuit.



Karnaugh MappingKarnaugh Mapping, or K-mapping is simply another method to simplify logic expressions in a more graphic and visual fashion. K-mapping uses groups of positive outputs to simplify expressions. These groups consist of adjacent 1’s in the truth table that are then converted to a logic expression. This method is very effective and sometimes more efficient then Boolean Algebra.

A simple K-Map example



NAND/NOR LogicSometimes there is a more effective implementation than AOI logic. That’s where NAND and NOR gates come in handy! A NAND gate is an inverted AND gate and a NOR gate is an inverted OR gate. Sometimes NAND and NOR implementations can utilize less Integrated Circuits (IC’s) and therefore be cheaper for the production of circuits.

This compares the equivalent AOI and NAND circuit. The NAND is more efficient because it only uses one IC.



Fireplace ProjectA company requires a new system to monitor their fireplaces because their safety systems are ineffective. There are 4 flames and a sensor for each one. The emergency cut off valve should be triggered whenever less than 3 sensors detect no flame to ensure no gas is escaping. An indicator should be activated whenever all of the sensors do not agree to indicate there is a problem with the sensors.

Diagram of Fireplace



Fireplace Project (Cont.)This project culminated almost all of the concepts learned previously in this course. First the truth tables and logic expressions were derived with K-Mapping. Then the two sections of the circuit were constructed in the CDS software to test its function. One section used AOI logic and the other used NOR logic. The circuit was finally recreated on a breadboard.

Final Circuit in CDS program



2.3 Introduction to Date of Birth Project

The majority of unit 2.3 is the Date of Birth project along with some lessons that help complete that project. Students will learn how to utilize seven segment display and demonstrate their usage in the Date of Birth project. This unit will again culminate almost all prior knowledge both for review but also because of their necessity.

Seven Segment Displays Date of Birth Project



Seven Segment DisplaysSeven segment displays are used in everyday life almost everywhere. A seven segment display is a set of 7 LED’s combined in a pattern That allows for the display of numbers and letters. There are two types of seven segment displays: anode and cathode. The difference involves whether ground or power determines the lit position. Seven segment displays also use a clever method to conserve power by quickly cycling between LED’s that must be so that we observe all segments are on. In reality, only one segment remains lit at a time.

Seven Segment Display



Date of Birth Project

The objective of this project is to display the month, day, and year of one’s birth using one 7 segment display and 3 inputs. This is done by splitting each segment of the display into a different section of the circuit. In other words, each segment has its own truth table and logic expression. My birthday is 07-31-97. First, the truth table and logic expressions were derived using K-maping. Then the circuits were creating including 2 NAND and 2 NOR circuits. This circuit later utilized the programmable logic board.

Final CDS Circuit



2.4 Specific Combinational Logic Circuits & Misc.

This Unit is a transitional unit between combinational logic and sequential logic. This is used to cover materials that do not fit in with other topics such as various number systems , binary addition, and Multiplexers and Demultiplexers. XOR and XNOR gates are also utilized by student to increase efficiency of circuits when possible.

Octal & Hexadecimal Number Systems

XOR/XNOR Logic

Multiplexer/Demultiplexer

Binary Addition

2’s Compliment Arithmetic



Octal & Hexadecimal Number Systems

Computers need an awful lot of data to function at the capacity they do, and if binary were solely used, computers would be slow and full of glitches. That is why the Octal (8) & Hexadecimal (16)Number systems are helpful; they compact long sequences of binary to create 8, 16, 32, 64, 128, ect. bit systems. So as with binary, converting between the decimal, octal, and hexadecimal number systems is necessary. Since there are only 10 possible numbers to use as digits, letters are needed for the hexadecimal number system.

Graphic to describe conversions between number systems



XOR/XNOR LogicXOR and XNOR are two more gates that are used to create higher efficiency whenever possible. The XOR gate is used to create “X-clusiveness”. In the OR gate, at least one input must be active. In XOR not all inputs can be to output a positive. XNOR is the opposite of XOR. All positive outputs in the XOR gate will be negative in the XNOR gate, and vice versa. This logic is commonly used to create binary adders.

Example XOR Logic Circuit



Multiplexer / Demultiplexer

A multiplexer is a device that allows for one source to have many destinations. This is attained by using a set of switches to decide where the source . A Demultipllexer does the opposite of a Multiplexer. It takes multiple sources and allows it to travel to many destinations. The amount of switches corresponds with how many outputs/inputs there are for that specific IC.

Practical use of a Multiplexer



Binary AdditionAdding binary is similar to adding decimal numbers but slightly different. One has to keep in mind that the max number in a given digit is 1, anything above that must be carried to the next digit. Binary can also be added within circuits using half or full adders. Half adders only have 2 inputs and 2 outputs and can only be used for the last digit (least significant digit). The Full adder has 3 inputs and 2 outputs and can be strung together to add large numbers.

Example of an Adder Circuit



2’s Compliment Arithmetic2’s Compliment Arithmetic is needed when adding negative binary numbers. In binary, a negative sign cannot be placed before a binary numeral. For this reason this method is used to switch between positive and negative binary values. To switch between positive and negative, the individual digits must all be changed to their opposite (ex. 1 to 0, 0 to 1). Then the new numeral must be added to 1 using binary addition

Example of Displaying the number -5 in binary



2.5 Programmable Logic: Combinational

This unit deals almost solely with the Programmable abilities of both the Computer Design Software and the Field Programmable Gate Array. The information learned in lessons will be culminated in the Paper Jam project which will also use topics from throughout the unit.

Programmable Logic Device Paper Jam Project



Programmable Logic Device

In previous projects, if one wanted to use actual hardware to display a project, the breadboard must be completed using all the individual components. With a Programmable Logic Device, CDS circuits can be exported to the board so that hardly any hardware is needed to be built to see the physical results of the circuit. This feature was utilized with the Date of Birth Project as it was exported to the board to display the birth date on its 7-segment display.

Programmable Logic Device



Paper Jam ProjectThis project required the designing of a circuit that detected paper jams in a copier. It utilized 3 switches that the paper would activate. When 2 adjacent switches are active, an LED and Buzzer must be activated. When the jam is cleared, the LED must turn off but the buzzer should remain on until a clear switch is pressed. This project is an introduction to sequential logic with the clear function as well as a demonstration of the Programmable Logic Device.Visual Representation of Truth

Table



Unit 3: Sequential LogicThis Unit will cover all the basics of sequential logic.. Sequential logic differs from combinational logic in that it includes a memory portion. This unit will cover flip flops, latches, counters, state machines and more. The projects in this unit utilize not only the new information covered, but also combinational logic and breadboarding learned in previous chapters. This unit few individual lessons and projects due to the complex nature of each. Therefore there will be no sub-unit slides for this unit.

Flip Flops

Latches

Flip Flop Applications

Asynchronous counters

7 Segment Display Driver

The 74LS93

Synchronous Counters

Now Serving Project

Toll BoothMSI Gates

State Machines

3.2 Asynchronous Counters

3.1 Latches & Flip Flops

3.3 Synchronous Counters

3.4 State Machines



Flip FlopsFlip Flops are critical to Sequential Logic and provide the memory element to distinguish it from combinational logic. Flip flops have essentially two types of inputs, the actual data input and the clock input. The output of flip flops change on either the rising or falling edge of a clock pulse based on the data input. There are two types of flip flops: D and J/K. In a D flip flop the output (Q) copies the input D on the corresponding clock edge. In a J/K, two inputs dictate whether the output (Q) toggles, is set to high, is cleared to low or does not change.

D Flip Flop

J/K Flip Flop



Latches

A Latch has an Enable input (EN) which, when active, holds the current output. The enable function disregards whatever the D input is reading. In other words, the EN input on a Latch is level sensitive, and on a flip flop the clock is edge sensitive.

D-Latch



Flip Flop ApplicationsFlip Flops have many applications including an event detector. An event detector holds a signal until the event that changed the signal is addressed. A data synchronizer is used to hold individual inputs until the correct time, to make sure all inputs are timed in synch. A frequency divider can divide an input frequency by multiples of 2. A shift register is a group of flip flops that shift values from one flip flop to the next for every clock pulse.

An example of a shift register

The function of a Data Synchronizer



Asynchronous CountersBy connecting flip flops together, a counter can be made. The flip flops are connected so that the clock is either connected to the Q or Q’ depending on whether the clock is an up or down counter. The amount of values that can be displayed is equal to 2 to the power of the number of flip flops. For example, if there are 3 flip flops, 8 values could be displayed. Upper and lower limits can also be set using a little combinational logic and the clear and preset options.

Asynchronous Counter



Seven Segment DriverThe 74LS47N IC can take the input from a binary counter and output what is necessary to display the value on a seven segment display. This combined with some resistors is very useful to counters

Counter using the Seven Segment Driver



The 74LS93This IC is an Asynchronous MSI counter or a 4-Bit ripple counter. It is called a ripple counter because there is a slight timing delay due to the clock being connected only two the first flip-flop. This IC allows a 4-Bit counter in one package but includes some limitations. These include no lower limit and no down count option.

A Simple Circuit using the 74LS93



Synchronous CountersSynchronous counters accomplish the same thing that Asynchronous counters do but have a few differences. One is that each flip flop is individually clocked and therefore there is no ripple effect. Synchronous counters do require more logic than Asynchronous ones though.

A 3-Bit Synchronous Counter



MSI GatesThe 74LS163 is a 4-Bit Synchronous Counter that has an up count, a pre-loadable count start, a synchronous load, a synchronous clear, two enable inputs, and a carry out signal. The 74LS193 is similar to the 163 but also has down counting, a Borrow-Out signal, and asynchronous load and clear.



Now Serving ProjectThis project was designed to utilize previous knowledge of counters to create a deli counter, that is a counter with a range of 0-99. For this to occur, two counters are needed, one counter in the ones digit and one for the tens digit. First, the circuit was built in Multisim and then exported to the DLB. This counter also included a next button to advance the count and also a reset button to set the count back to 0. The Active Now Serving Circuit



State MachinesA state machine is a synchronous sequential circuit, consisting of a sequential logic section and a combinational logic section, whose outputs and internal flip-flops progress through a predictable sequence of states in response to a clock and other input signals. State machines can be visualized using a state graph, which is essentially a truth table but with a more graphic representation. A state machine has an input combinational logic section, a memory section, and an output combinational logic section. This state machine was used in a project to display the last 4 digits of our phone number.

A State Graph



Toll Booth ProjectThis project uses knowledge of state machines and combinational logic as well as sequential logic. The goal is to create a toll booth arm that moves up and down when the corresponding switch is pressed and displays whether the gate is open or closed using an LED. This project was first layed out using a state machine and then transferred into Multisim. The finished circuit was then exported to the DLB. Some breadboarding was completed to allow a connection between the programmed board and the VEX toll booth arm.

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