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The previous blog post focused on generalized number bases – an essential concept of electrical and computer engineering (ECE) that is often not covered well at the high school level. Another area where pre-college preparation often falls short of college ECE expectations is the relationship between frequency, period, and wavelength for electromagnetic waves. This is often covered briefly in high school physics and chemistry courses, but those courses typically use scientific notation instead of engineering units. As a result, students cannot mentally translate among engineering units of frequency, period, and wavelength at conversational speeds.


Relationship between frequency, period, and wavelength

As a reminder, this table summarizes the basic relationships between frequency, period, and wavelength of electromagnetic waves in a vacuum.






Word / Abbreviation


Word / Abbreviation



Hertz (Hz)


Second (s)

300,000 km


Kilohertz (kHz)


Millisecond (ms)

300 km


Megahertz (MHz)


Microsecond (μs or us)

300 m


Gigahertz (GHz)


Nanosecond (ns)

300 mm


Terahertz (THz)


Picosecond (ps)

300 μm


Petahertz (PHz)


Femtosecond (fs)

300 nm


Applications – RF, circuit boards, and design validation

Engineers discussing wireless signals may talk about a 2.4-GHz signal, and it is helpful to be able to think of the associated period as being a bit more than 400 picoseconds. Similarly, a 5-GHz signal has a 200-picosecond period. Given the increasing diversity of radio frequency (RF) applications, especially those associated with the growing Internet of Things (IoT), an intuitive understanding of frequencies and their various physical properties is helpful to ECE students.


This concept is also critically important in designing circuit boards and interconnects. Electromagnetic waves propagate at approximately 3×108 meters per second (the “speed of light”), so the wavelength of a 1-GHz signal in a vacuum is 30 cm (about one foot). Depending on the physical material, the propagation speed of a signal in a circuit board or cable may be significantly slower, so seemingly minor changes in circuit layouts can cause significant propagation delays and timing challenges in high-frequency circuits.


Furthermore, understanding this concept is helpful in design validation. For example, suppose you need to measure a signal’s edge with a rise time of 15 nanoseconds. How fast must you sample that waveform to accurately catch that edge, including overshoot and any ringing that may occur? Facility with mental math will help you make correct test choices quickly.


The fundamental arithmetic of electromagnetic waves occurs with great frequency in ECE coursework and in professional practice after college. The high school student who becomes adept with the various relationships in engineering units will start ECE studies with a significant advantage.

A motivated high school student can usually obtain appropriate high school math preparation for an electrical and computer engineering (ECE) or computer science course of study. Algebra, geometry, trigonometry, and calculus are widely available in many high schools, and these are mostly sufficient for a freshman engineering student.


However, some topics needed for ECE are often covered briefly at best in the secondary math curriculum. One such topic is generalized number bases, including binary, hexadecimal, and octal numbers. A surprising number of freshman ECE students, even at highly respected universities, have no idea how to convert among numbers expressed in the following bases:













Overview of binary numbers

Binary numbers are the basis of modern computers, which use 0 and 1 to represent OFF and ON states in digital circuits. Just as the decimal number system uses the ten digits 0 through 9, the binary number system uses the two digits 0 and 1. For example, a binary number might be written as shown below.

Figure 1: A binary number


In addition, just as the place values of the base ten system are 100, 101, 102, 103, 104, and so on, the place values of base 2 begin with 20, 21, 22, 23, 24, as shown below.

Figure 2: A binary number with base ten place values


Therefore, the value of the binary number above is the sum of the place values with 1’s in them:

Value of binary number = 32,768+16,384+4,096+1,024+512+256+8+2 = 55,050


Overview of octal and hexadecimal numbers

One challenging aspect of binary numbers is that they are long and difficult to read. While it is easy to read “fifty-five thousand, fifty”, the number “one, one, zero, one, zero, one, one, one, zero, zero, zero, zero, one, zero, one, zero” is a bit awkward (apologies for the pun).


To reduce the awkwardness of binary numbers, we often group binary digits into groups of three or four digits from right to left. Groups of three bits are represented as 0 to 7 (octal), and groups of four bits are represented as 0 to F (hexadecimal), as shown below.



Three Bits


Four Bits







































































The place values of octal numbers are 80, 81, 82, 83, and so on. We can therefore convert a binary number to octal three bits at a time and evaluate it as shown below:

Figure 3: Converting a binary number to octal, three bits at a time


Adding the numbers shown in the Product row, we see that the octal number 153412 is equivalent to the base 10 number 55,050.


A hexadecimal example

Finally, we can group the bits four at a time to convert them to base 16 (hexadecimal), as shown below.

Figure 4: Converting a binary number to hexadecimal, four bits at a time

Practice converting between bases

To practice these conversions, consider using Excel to generate test cases. Excel has 12 functions, named DEC2BIN, HEX2OCT, OCT2DEC, and so on that convert among the various number bases. You simply specify the input number and, in some cases, the number of digits you want in the output. For example, =DEC2BIN(185,10) converts the decimal number 185 into the 10-digit binary number 0010111001.



University ECE departments expect incoming students to understand number bases, but many students never receive appropriate instruction on this in high school. Students who are unfamiliar with these concepts should spend some time studying them before they arrive on campus to start studying ECE or computer science.

It is difficult for electrical and computer engineering (ECE) students to master the field’s many technical terms, abbreviations, and acronyms. While topics like resistance, capacitance, voltage, current, and power are typically covered in high school physics, freshman engineering students quickly find themselves studying mysterious concepts like Wheatstone bridges, Zener diodes, and Schottky transistors. To make things even more challenging, engineers frequently speak and write with abbreviations. Students are soon overwhelmed by BLE, IEEE 802.11 a/b/g/n/ac/ad/af/ah/ai MAC and PHY, WLANs, LPWANs, RFID, 900-MHz RF, 2.4-GHZ RF, ISM bands, and IoT RF and BDA. This blog post will cover three ways students can get help ASAP, before their GPA is affected!


Jameco Electronics glossary

Jameco Electronics has a helpful electronics glossary at It contains 372 concisely defined terms, with typical definitions roughly 12 to 20 words long. This glossary tends to focus on technical concepts of electronic circuits, with relatively few acronyms and abbreviations. The whole glossary is presented as a single list, which makes it easy to print for offline use.


Maxim Integrated glossary

Maxim Integrated has a much larger glossary (1,040 terms) at This is also presented as a single list, but it is probably longer than most people would want to print. This glossary is not as concise as the Jameco Electronics glossary, but it includes richer details that connect the various concepts to each other and to the history of electronics. The Maxim Integrated glossary also includes many abbreviations and hyperlinks to detailed articles.


Hobby Projects glossary

A third glossary is available from Hobby Projects at It is closer in size to the Maxim Integrated glossary, but its selection of terms and concise writing style more closely resemble the Jameco Electronics glossary. Unlike the other two glossaries, the Hobby Projects glossary has a separate HTML page for each letter of the alphabet, which makes it lessfriendly for scrolling and printing. The Hobby Projects glossary is just a small part of a very large reference site that also includes a schematics symbol reference (, a list of electronics formulas (, a list of abbreviations (, and much more.



A key to success in any field is understanding the jargon of the discipline, and this is particularly important in ECE. By referring frequently to the tools listed above, students can quickly climb the learning curve and understand instructors’ lectures and textbooks in greater depth.

One challenging aspect of electrical and computer engineering (ECE) is that electrical current is inherently difficult to visualize. Mechanical engineers see things spin and bend; chemical engineers see color changes and crystallization, and civil engineers often work on huge projects that can be seen from airplanes. ECE students, on the other hand, must use their imaginations to visualize current flow, capacitance, and inductance.

To help students visualize electronic circuits, Paul Falstad has created an outstanding electronic circuit simulator applet (

Figure 1: Paul Falstad’s Electronic Circuit Simulator Applet

The applet produces vivid animations of current flowing through circuits, and as you can see above, you can adjust sliders to modify the circuit’s LRC values. You can also open and close switches. For example, in the image below, the user has closed the switch at the top of the circuit and moved the LRC sliders, resulting in changes to the waveforms.

Figure 2: Circuit with switch closed and modified LRC sliders

Beyond basic LRC circuits

If the circuit simulator could only simulate LRC circuits, it would be a useful tool. However, LRC circuit simulation is only one of the applet’s many capabilities. To get a sense of the applet’s breadth, click the Circuits menu and explore the various sub-menus, as shown below.

Figure 3: Circuits menu

In this case, we followed the menu path Circuits > Transistors > Oscillators > Hartley Oscillator. The circuit for this oscillator is shown below.

Figure 4: Hartley oscillator circuit

Add circuit components

As if all these circuits were not enough, author Paul Falstad thoughtfully included the ability to add components to circuits via the Draw menu.

Figure 5: Draw menu

Students can choose from well over 100 components, and many of the components have customizable values. For example, you can edit the resistance of a resistor, and you can specify various parameters associated with an AND gate, as shown below.

Figure 6: Editable fields for an AND gate

In summary, Paul Falstad has produced an outstanding animation tool to help students understand electronic circuits. The huge variety of circuits simulated and the richness of the app’s feature set provides virtually limitless opportunities for student experimentation and learning.

A previous blog post in this series highlighted the free circuits textbook from the Free Electrical Engineering Textbook Initiative. The initiative is a joint effort among experienced, highly respected professors from the Universities of Michigan, Utah, and California, Berkeley.


In addition to the circuits textbook, the initiative has produced a free image processing textbook, Image Processing for Engineers, available as a 438-page PDF file at The book is co-authored by Dr. Andrew E. Yagle and Dr. Fawwaz T. Ulaby, both from the University of Michigan. Dr. Yagle is a Professor Emeritus of Electrical Engineering and Computer Science, and Dr. Ulaby is currently a professor in the ECE Division of the College of Engineering.



Figure 1: Image Processing for Engineers cover


The rapid proliferation of digital cameras and imaging sensors of all kinds has made image processing an increasingly important part of the electrical and computer engineering field. This is particularly true in medical, smart vehicle, security, and national defense applications, where both static and video images captured in various parts of the electromagnetic spectrum are now essential tools.


Like the Circuit Analysis and Design book, Image Processing for Engineers is a clearly-written and well-illustrated textbook. It is best suited for an upper-level undergraduate course or early graduate course because the reader is expected to know multi-variable calculus, advanced linear algebra, about one year of college-level statistics, Fourier transforms, and Laplacians.


The book’s twelve chapters cover the following topics:


  1. Imaging Sensors
  2. Review of 1-D Signals and Systems
  3. 2-D Images and Systems
  4. Image Interpolation
  5. Image Enhancement
  6. Deterministic Approach to Image Restoration
  7. Wavelets and Compressed Sensing
  8. Random Variables, Processes, and Fields
  9. Stochastic Denoising and Deconvolution
  10. Color Image Processing
  11. Image Recognition
  12. Supervised Learning and Classification


In addition to the PDF file, the book’s companion site ( includes answer keys for the book’s concept questions and exercises. It also includes MATLAB files and JavaScript programs that supplement the text.

Possible topics for the authors to consider for future editions include basic video image processing, real-time imaging, and digital watermarks. Topics related to the physical “processing” of light waves at or even before the sensor, such as white balance, color appearance models, spherical aberration, and chromatic aberration might also be helpful. These topics are beyond the scope of the present text, but they are important to successful imaging.

In summary, Image Processing for Engineers is a mathematically sophisticated, clearly presented textbook on an important topic. Its text, graphics, exercises, and comprehensive companion Web site make it appropriate for adoption by universities and for self-study by working professionals.

This is a follow-up to the previous post on how you can create CCDF charts quickly, and for free. That post ended with a nice-looking CCDF chart, shown below.

Figure 1: CCDF Chart


While this chart is correct, it may be misleading to the reader, because the dramatic drop appears between -5 and -6. Although these current levels (1 to 10 µA) are where the device spends most of its time, they are NOT where the device spends most of its battery charge. Low current levels, even if sustained for relatively long periods of time, may be relatively insignificant. For example, a 10-mA current spends battery charge 10,000 times as fast as a 1-µA current. The purpose of this blog post is to continue the previous discussion and show you how to produce a CCDF-like chart that more accurately reflects how charge is consumed at different current levels.


STEP 1: Compute the total charge consumed and count down from 100%

Begin by re-sorting the data by column A. Calculate the total current in column C in cell E1, using the formula =sum(c2:c48001). Make sure that you are using the original current data in column C, of course. In cell E2, enter the formula =E1-C2, and copy this to the bottom of the data set (row 48001). In cell F1, enter the formula =E1/E$1, and copy this formula to the bottom of the data set as well. Convert the formulas in columns E and F into values, and then convert the values in column C to their base 10 logarithms as described in the previous article. Your spreadsheet should appear as shown below.


Figure 2: Counting down total current, starting at 100%.


Step 2: Create the chart

Sort the data by the Select and Sorted columns as described in the previous blog post to limit the amount of data to be graphed. Create an X-Y chart, using columns C and F as the X- and Y-axes, respectively.


Figure 3: Charge consumption chart


Step 3: Zoom in  by setting upper and lower limits on the X-axis

In the chart above, the graph is essentially flat to the left of -3 on the X-axis, and it is 0 to the right of -2. Therefore, we can zoom in by setting the X-axis limits to -3 and -1.9, as shown here.

Figure 4: Charge consumption chart zoomed in to show detail


Step 4: Use the tooltips to precisely identify important current levels

Hover your mouse over areas where the charge curve drops quickly. In this case, you can see that much current is being consumed at 10^-2.03 A. This gives you insight as to where you have a good opportunity to improve the charge consumption of your device.

In conclusion, the CCDF chart is a very useful tool, and you do not need to spend money on special software to create one. By showing the charge consumption rather then the time consumption, you can get quick insights into your device's behavior that will help you to optimize your design for long battery life.

There is an obvious, longstanding trend in electrical and computer engineering (ECE) toward energy conservation and ever-longer battery life. This is especially true in applications related to the Internet of Things (IoT), where expectations of 5- and 10-year battery life for sensors are common. It is also true for battery-powered medical devices located with the human body, where changing a battery can be both expensive and risky.


One common tool for displaying how charge is consumed from a battery is the complementary cumulative distribution function (CCDF) chart, shown below.


Figure 1: CCDF Chart


We can see at a glance that the device under test (DUT) spends nearly all of its time at current levels above 1 µA, but less than 10% of its time at current levels above 10 µA. The other way to think about that is to say that the device spends about 90% of its time in at single-digit µA levels of current.


Many Keysight instruments, including the N6705, the X8712A, and the CX3300 Series can produce CCDF charts, but students often need to produce a CCDF chart when they either lack the necessary equipment or when the equipment is across campus, an inconvenient distance away. Fortunately, the student with good spreadsheet skills can create a CCDF chart in just a few minutes by following the procedure below.


Step 1: Load the data into the spreadsheet

Put the current reading data in column B, and number the rows in column A, as shown. The row numbers allow you to return the data to its original order after we sort it. In this case, we have 48,000 rows of data.


Figure 2: Data loaded into the spreadsheet and numbered


Step 2: Sort the data by value, number, and prepare to eliminate data

Sort the data in ascending order by current level. Then insert a new column A, and number the rows from 1 to 48,000. Finally, put the following formula into cell D2: =mod(a2,20). Then copy it down to the bottom of the data. This formula will count from 1 to 19, return to 0, and then count up to 19 again. This pattern repeats to the end. We do this because most spreadsheet software has difficulty graphing huge data sets, so we are going to select only every twentieth value.


Figure 3: Data sorted by ascending current levels.


Step 3: Bring every twentieth value to the top of the list

Sort the data by the Select and Sorted columns. As you can see in column A below, this brings every twentieth value to the top of the list for easy graphing.


Figure 4: Every twentieth value at the top of the list


Step 4: Change column D to represent portion of time remaining.

In cell D2, change the formula to: =1-A2/48000. This will indicate the portion of measurements remaining as a number decreasing from 1 to 0. Copy the formula down until it hits 0, which will be in row 2401.


Figure 5: Count portion of measurements remaining down from 1 to 0.


Step 5: Replace the values in column C with their base 10 logarithms

Given the highly dynamic nature of current in many IoT devices (sleep in nA or µA and operation in mA), it usually makes sense to replace the data in column C with their base 10 logarithms. In cell E2, type =log10(C2) and copy this formula down to row 2401. Then copy and paste the values from column E over those in column C.


Figure 6: Values in column C replaced with their base 10 logarithms


Step 6: Create an X-Y line graph out of columns C and D

At this point, you are ready to create the CCDF chart. Use the X-Y (scatter) plot feature on the range C2:D2401to create the graph shown below.


Figure 7: Basic CCDF chart created from 2400 rows of columns C and D.


Step 7: Label the graph and format the axes

Even though the graph in Figure 7 is correct, it is generally worth taking a minute or two to improve its appearance. Edit the axes and the various labels to improve the readability of the chart, as shown below. You may also want to turn on the grid lines, but remember not to be misled by the logarithmic nature of the X-axis.


Figure 8: CCDF chart with better labeling for improved readability



The CCDF chart is very useful in summarizing how frequently a device under test spends its time at various current levels. By following the simple procedure outlined above, you can create a CCDF of current data by using nothing more than commonly available spreadsheet software.

If you will pardon the pun, an electrical and computer engineering (ECE) student must be solidly grounded in mathematical analysis to succeed in calculus, differential equations, Laplace transforms, and other areas of high-level mathematics. Fortunately, one of the classic, proven texts in the field, Principles of Mathematical Analysis, is available for free in several electronic file formats at

Written by the late, great Walter Rudin of the University of Wisconsin, Principles of Mathematical Analysis has been a well-respected textbook for well over 40 years, and it is admired for its clear and concise prose style. The book is nearly devoid of graphics, and it would certainly not win any awards for production values. However, it is a clear and thorough introduction to the field of mathematical analysis, with the following eleven chapters:


  1. The Real and Complex Number Systems
  2. Basic Topology
  3. Numerical Sequences and Series
  4. Continuity
  5. Differentiation
  6. The Riemann-Stieltjes Integral
  7. Sequences and Series of Functions.
  8. Some Special Functions
  9. Functions of Several Variables
  10. Integration of Differential Forms
  11. The Lebesgue Theory


Not all of these topics are required for an undergraduate ECE student, but most are useful background, and it is good to have a quick way to learn should an unexpected topic appear in a class.


A separate answer key, written by Roger Cook of the University of Vermont, is available at

An electrical and computer engineering (ECE) student studying waveforms, noise, and signal modulation must generate and view a signal. Lab equipment is sometimes in short supply, and if no function generator is available, there may be no signal to view.


Fortunately, many Keysight InfiniiVision X-series oscilloscopes can generate a wide variety of training waveforms. Press [Help] > Training Signals, to select from a menu of training signals:


Then connect a 10:1 probe between the [Demo Probe Comp] output (including ground) and the channel [1] connector. This enables you to work with the training signal.

In addition, some Keysight oscilloscopes have built-in waveform generators. Look for a G on the end of the product number, such as EDUX1002G. In the 1000X series, the EDUX1002G and the DSOX1102G have a built-in waveform generator.


The higher performance models (2000/3000/4000/6000 X-series) all have the waveform generator built in, but it requires a license to be enabled. The easiest way to check is to push the [Wave Gen] button on the front panel; if it lights up, it is enabled.


The oscilloscope’s front panel contains the waveform generator’s [Gen Out] output connector and a [Wave Gen] key to configure the waveform generator.


After you press [Wave Gen], press the Waveform or Settings softkey to configure the waveform and its output hardware.




Sine, Square, Ramp, Pulse, DC, or Noise


Logic Preset: TTL, CMOS . . .

Enable/disable waveform

Output impedance: High-Z or 50 Ω

Sync trigger

Add noise

Modulation: Frequency (FM), amplitude (AM), frequency-shift keying (FSK)


You can also program the waveform generator with the Standard Commands for Programmable Instruments (SCPI) language. The instrument’s display provides clear feedback to help students quickly learn about various waveforms, modulation, the SCPI programming language, and the oscilloscope.


Finally, note that you can press and hold any front-panel key to obtain help on that key. For example, here is the help associated with the [FFT] key.


You can also press the [Help] key to change the language in which the push-and-hold help is displayed.


When the language is set to Japanese, pushing and holding the [FFT] displays the following text.


In short, ECE students can use an inexpensive oscilloscope with built-in waveform generation capabilities to learn several fundamental concepts, learn how to use the instrument, and to replace a function generator for basic applications.

To help students and educators quickly learn to analyze a variety of signals with an oscilloscope, Keysight has put together an “Educators Kit” that can be used with all InfiniiVision oscilloscopes. This kit is available for free download at

The field of electrical and computer engineering (ECE) is very broad; some well-known universities require 134 credits or more for a bachelor’s degree. Even with that many credits, there is no way an undergraduate education can expose an ECE student to everything that may be required in industry.


One area that usually gets limited (if any) exposure is the making of highly accurate and precise parametric measurements on resistors, capacitors, diodes, and transistors in a semiconductor manufacturing process. Even if an engineer is not working on semiconductor manufacturing directly, concepts such as isolation, guarding, Kelvin (4-wire) measurement, and ground loop avoidance are valuable for in-circuit testing, whether in manufacturing or R&D design and validation.


To help students and working professionals learn these important concepts, Keysight engineer Alan Wadsworth has written The Parametric Measurement Handbook, now available for free download at In addition to updating technology and instrument references, the fourth edition adds an entirely new chapter on power device test.



Figure 1: Cover of The Parametric Measurement Handbook


The handbook begins by setting the context and history of parametric testing, and then it goes into basic parametric testing principles. These are followed by extensive chapters on source/monitor units (SMUs), on-wafer testing, and time-dependent and high-speed measurements. The last four chapters cover resistance, diodes and transistors, capacitance, and power devices. A brief appendix covers specific parametric measurement solutions, and this is followed by a glossary of key terms.


In short, the fourth edition of The Parametric Measurement Handbook contains a very thorough introduction to an important and challenging area of electrical engineering. Even if the reader never works in semiconductor manufacturing, the principles covered will apply to many areas of high-precision, high-accuracy electrical measurement and characterization.


Figure 2: Sample page from The Parametric Measurement Handbook



A college student recently told me that food at her school’s cafeteria costs about $132 per week, which is a considerable amount of money. The textbook for the introductory circuits class at the same school lists for $187, or roughly ten days of meals. Over the course of an electrical and computer engineering (ECE) major’s undergraduate career, technical textbooks could easily cost thousands of dollars, even for used textbooks. This expense may limit opportunity for some students.


Reducing expenses for students

To reduce these expenses, professors at the University of Michigan, University of Utah, and University of California, Berkeley, have collaborated on the Free Electrical Engineering Textbook Initiative to produce high-quality, free textbooks for ECE students. The books are distributed in PDF form, and instructors may obtain complimentary printed copies. Students may also purchase new, full-color printed copies for $60 to $75, depending on the page count.


One book in the series, Circuit Analysis and Design (, is co-authored by professors Fawwaz T. Ulaby (Michigan), Michael M. Maharbiz (California, Berkeley), and Cynthia M. Furse (Utah). Professor Ulaby is an IEEE Life Fellow, and a winner of both the IEEE Thomas Alva Edison Medal and the IEEE Education Medal. Professor Maharbiz co-invented "neural dust," which is an ultrasonic interface for very small body implants. His group also pioneered radio-controlled cyborg beetles, one of the MIT Technology Review’s top ten emerging technologies in 2009. Professor Furse is both a professor in the ECE department and an Associate Vice President for Research at the University of Utah. She is also a co-founder of LiveWire Innovation, a Utah-based technology company. In short, the three authors are highly accomplished individuals with extensive experience in industry, research, and teaching.

Figure 1: Circuit Analysis and Design cover


Thorough coverage of the topic

The book covers the typical topics that one would expect, including purely resistive circuits, RC and RL circuits, RLC circuits, op amps, filtering, AC power topics (including three-phase), and more. Each chapter begins with learning objectives and ends with a useful quick reference containing key concepts, formulas, and terms. There are problems for checking understanding at the end of each of the 13 chapters – over 800 problems in all.

Figure 2: Chapter summary


The book assumes knowledge of basic integral and differential calculus in some areas, but other topics will be clear to the student with a solid grounding in pre-calculus high school mathematics. The last two chapters cover Laplace transforms and Fourier analysis; these naturally require a very strong math background.


Connecting students to applications

In addition to the typical circuit topics, the book includes 32 technology briefs, which are typically two- to five-page articles on ECE applications. Sample topics include nanotechnology, IC fabrication, RFID tags, audio electronics, and synthetic biology. While the rest of the book does not require information contained in the technology briefs, the student will benefit from reading them to understand the current state of the profession and its opportunities. In addition, some technical topics (for example, 2- and 4-wire measurements) are only covered in the technology briefs.


Figure 3: Technology brief 


The technology briefs are available as standalone articles on the book’s companion Web site, which also includes answers to the book’s concept questions and exercises. An interesting “Test Your Understanding” feature checks student understanding of any chapter by creating an  quiz of five questions randomly selected from a database.



The book is generally very well done, but it has little to no hyperlinking. The user can use the bookmarks feature in the reader to jump to the beginning of specific chapters and appendices, but additional hyperlinks would be useful in navigating quickly through this 795-page book. That quibble aside, Circuit Analysis and Design is an excellent text for typical circuit analysis classes, and ECE departments who adopt it will save their students significant money without compromising quality. They may also find that their students do better on tests if they use the  quiz generators.


ECE Student Success Toolkit

Posted by BradJolly Employee Aug 13, 2018

Opportunities for electrical and computer engineering (ECE) graduates seem to be virtually unlimited, with growth in health and medical devices, Internet of Things, consumer electronics, supercomputing, artificial intelligence, cybersecurity, smart energy, electric vehicles, robotics, cloud computing, augmented and virtual reality, 5G, machine vision, and much more. Despite all this opportunity, the completion rate for ECE majors remains among the lowest of the engineering disciplines.


To help more students succeed, this blog will feature a series of blog posts to arm students with free tools and tips to help students meet the challenges of an ECE education. Please add your ideas in the comments; perhaps they will be featured in a future blog post. Who knows how many students might be helped by your kind sharing?

The most recent blog post discussed  the book Make it Stick, the Science of Successful Learning, by Henry L. Roediger III, Mark A. McDaniel, and Peter C. Brown. The authors’ intent is to replace the theory, lore, and intuition that underlies much current learning theory with scientifically tested facts.


The problem with current learning theory is that it encourages unproductive practices. For example, massed practice, re-reading texts, and teaching in students’ preferred learning styles simply do not work well, according to the authors.


What does work?

Fortunately, the authors provide several solutions to improve learning that are based on scientific research. Here are just a few of the key ideas.


  • Retrieval practice, such as flashcards, is more effective than re-reading.
  • Periodic practice is more effective than massed practice.
  • Interleaving topics is more effective than focusing on one topic at a time.
  • Attempting to solve problems before being taught the solution is helpful.
  • Frequent, low-stakes testing helps calibrate the learner’s judgment about learning effectiveness.
  • Learners should be encouraged to elaborate on what they are learning, using their own words and connecting the new material to existing knowledge.

There is much more to the book than these two blog posts can contain, and the structure of the book itself uses many of the techniques that the authors advocate. Teachers and students of all ages should read this book and use its key ideas to improve learning outcomes.


Making Learning Stick

Posted by BradJolly Employee Apr 9, 2018

A frustrated elementary school teacher recently told me of her exasperation with teaching math. Just a week before the school’s mandated standardized tests, she had repeatedly drilled her students on adding and subtracting fractions, and nearly every student scored well on her chapter test. Yet when the students took the standardized test, the same students performed dismally on adding and subtracting fractions. “It was as though they had never seen the concepts,” sighed the frustrated teacher.


This experience is common at all levels of education; every parent and teacher has seen seemingly solid mastery disappear like cotton candy in a hurricane. To address this frustration, cognitive psychologists Henry L. Roediger III and Mark A. McDaniel joined novelist Peter C. Brown to write the book Make it Stick, the Science of Successful Learning. Brown and McDaniel were invited to deliver keynote addresses at the recent ECEDHA Conference in Monterey, because even professors at top universities see the need to improve their students’ learning.


The book begins with the observations that learning requires memory, that it is important for people to keep learning throughout life, and that learning itself is an acquired skill. Unfortunately, people have a very limited understanding of how to learn, as much of the received wisdom on learning is based on theory, lore, and intuition rather than scientifically tested facts.


Where received wisdom is wrong

Here are just a few of the problems that the authors identify:


  • Teachers rely on massed practice, such as worksheets with dozens of problems.
  • Students believe that re-reading will help them learn the concepts presented in the text.
  • Students believe that they can intuitively tell when they are learning effectively.
  • Teachers strive to teach students in the students’ preferred learning styles (auditory, visual, kinesthetic, and so on).
  • Students believe that if they study diligently in a way that works for them, they will find success.


Unfortunately, these beliefs and practices are either unsupported by data, or even counterproductive. The book’s solutions that make learning stick will be the subject of the next blog post.

The first and second blog posts in this series described divisibility rules for 11, 7, and 21. To summarize:






Chop, subtract


347 – 6 = 341

34 – 1 = 33

7 or 21

Chop, double, subtract


295 – 8 = 287

28 – 14 = 14


These rules work because adding or subtracting multiples of n does not change whether a quantity is divisible by n. The “chop, subtract” procedure subtracts a multiple of 11, and the “chop, double, subtract” procedure subtracts a multiple of 21 because it subtracts from the ones digit and TWICE from the tens digit (1+2×10 = 21). Every multiple of 21 is also a multiple of 7, so “chop, double, subtract” works for both 7 and 21.


If “chop, subtract” subtracts a multiple of 11, and “chop, double, subtract” subtracts a multiple of 21, then “chop, triple, subtract” and “chop, quadruple, subtract” subtract multiples of 31 and 41. Therefore, we can expand our list of divisibility rules as shown below.






Chop, subtract


347 – 6 = 341

34 – 1 = 33

7 or 21

Chop, double, subtract


295 – 8 = 287

28 – 14 = 14


Chop, ×3, subtract


102 – 9 = 93

9 – 9 = 0


Chop, ×4, subtract


213 – 8 = 205

20 – 20 = 0

17 or 51

Chop, ×5, subtract


698 – 35 = 663

66 – 15 = 51

5 – 5 = 0


Chop, ×6, subtract


317 – 12 = 305

30 – 30 = 0


Chop, ×7, subtract


653 – 14 = 639

63 – 63 = 0

27 or 81

Chop, ×8, subtract


221 – 32 = 189

18 – 72 = 54*

13 or 91

Chop, ×9, subtract


211 – 81 = 130


Chop, ×10, subtract


1535 – 20 = 1515

151 – 50 = 101

37 or 111

Chop, ×11, subtract


799 – 22 = 777

77 – 77 = 0


Chop, ×12, subtract


980 – 12 = 968

96 – 96 = 0

67 or 201

Chop, ×20, subtract


542 – 140 = 402

40 – 40 = 0

43 or 301

Chop, ×30, subtract


137 – 180 = 43*


Chop, ×40, subtract


1122 – 320 = 802

167 or 501

Chop, ×50, subtract


1035 – 200 = 835

83 – 250 = 167*

* In these algorithms, subtraction always yields the positive difference.


Note that some rules apply to multiple numbers. That is because the rule subtracts a multiple of the larger number, and the smaller number is a factor of the larger number. For example, the “Chop, ×5, subtract” rule applies to 17 and 51 because the rule subtracts multiples of 51 and every multiple of 51 is also a multiple of 17.


The rules above go well beyond the "2, 3, 4, 5, 6, 9, 10" list that students typically learn. They are easy to remember and to understand, and they deepen students' understanding of why divisibility algorithms work in the first place. Parents and teachers should consider exposing students to these rules.