Digital Concepts Series Two

A SYLVANUS DONAIE PUBLICATION

A NEW APPROACH TO TEACHING GROWN FOLKS

THE DIGITAL CONCEPTS +

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Series Two A Paradigm Shift – The Numbering System Written by Sylvanus Donaie BA, BSEET, MTM, MPM, MBA

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A NEW APPROACH TO TEACHING GROWN FOLKS

THE DIGITAL PROCESS Written by

SYLVANUS DONAIE About the Author

Since 2001, Professor Donaie has been transforming adult students into frontiers of their career, creating qualified project managers, and electronics engineers and technicians with undergraduate degrees. Having taught at many colleges and universities, he takes into his classrooms, labs and online platforms a broad range of experiences in electronics, computer, networking, refrigeration, and mathematics.

Sylvanus engineered and managed many key projects including designing XM Satellite Radio Terrestrial Repeater System and wireless/land-based system for Level 3, BellSouth, Fluor Daniel, AT&T, Verizon, Sprint and Time Warner. As a Training and Development Engineer, he led the development of the Process Safety Management (PSM) objectives for many refineries, creating training guides, operation manuals, maintenance manuals, operating procedures, self-study questions, PFD, and unit evaluations on crude units, fluid catalytic cracker plants, vacuum units, alkylation units, coker plants, refrigeration units, sulfur recovery and gas plants, and wastewater treaters.

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TRAINING AND DEVELOPMENT

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Twelve Part Series

Series 1. Introduction.

Series 2. A Paradigm Shift – The Numbering System.

Series 3.

What the Hell is Binary, Octal, and Hex?

Series 4.

Binary in an Electrical Representation.

Series 5.

Having a Logical Mind - Logic Gate.

Series 6.

Marching Lock Step – Counters and Clocks.

Series 7.

A Surprise of Addition – Adders and Comparators

Series 8.

Waving the Flags - Encoding and Decoding.

Series 9.

The Parking Lot - Addressing and Storage.

Series 10. The Bus System – Multiplexing/Communication.

Series 11. The Manipulator – Microprocessor/Microcontroller.

Series 12. What’s Next.

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INTRODUCTION Digitalization is not a new phenomenon. It’s as old as mankind; a brilliant process used for distant communication. Some groups used the drum beats to echo sounds of long and short notes while others used smoke with long and short puffs. However, with the advancement of the telephone and telegraph, the digital concept was side-stepped to more practical analog technologies.

Even today, sea vessel uses an older digital method of flashing light and loud sound signals in a Morse code format to communicate between itself and another vessel or station.

So why the resurgent? For the past hundred years, scientist (and more so due to market demands) gave the technology a closer look and moved it from the theory shelf to a practical marvel using electronics. As electronic components became smaller and more complex, the usage of digital technology increased. Simply put, because of digitalization, many electronic systems have been created with greater capabilities and faster performances and enhanced accuracy.

1 0 0 0 1

The early day of digitalize communication: the smoke signal Page 3

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According to a Brookings report, “By 2016, the share of jobs requiring high digital skills had jumped to 23 percent. The share requiring medium digital skills rose to 48 percent.

And in a huge shift, the share of jobs requiring low digital skills fell from 56 to 30 percent.”

Regardless of your profession, digitalization is transforming how you work, and having digital skills has become more of the rule rather than the exception. It’s a prerequisite for workers and businesses at large.

Here is the reality. For most technicians who were trained in an analog world, the digital system challenges them. I am seeing the exodus of car mechanics, HVAC and refrigeration techs, electricians, instrumentation techs, and even process operators to retirement or the unemployment lines. When it comes to anything digital, they run. Digital totally makes no sense to them. Those that remain in the field use guesswork and part swapping with very little troubleshooting techniques.

Worse, some technical schools are missing the benchmark on equally blending the theories and practicals of the legacy systems with modern digital electronics expertise. My experience in the field leaves me to sum up that students are being trained to be parts changers rather than receiving a wholesome education on operation, functionality, and troubleshooting.

With this publication, I will simplify the theories and the practical know-how of digitalization: an opportunity to highlight strengths that would be helpful on the job.

IN SERIES TWO...

In the next series, we will discuss the decimal numbering system. We use it as an acceptable system for our everyday essentials for counting and mathematical calculations. However, most know very little about its formation. And with good reasons!

Computers and digital systems use a different numbering system called binary. Persons who design, build, and maintain anything with digital electronics have to continuously maneuver their thinking between numbering systems. Those who can become great techs, and those who cannot run away.

I do not want you to run. As a result, I have developed techniques to simplify these systems to a first-grade level. I want you to have a simple understanding and to acquire some knowledge of our decimal numbering system. What is it? What is its role in today’s digital technologies?

In Series 3, look for to the talk on the backbone of the electronics digitalization: binary, octal and hex.

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Chapter One A Paradigm Shift -----

The Numbering System CONTENTS

The Decimal System Simple Addition in the Decimal System Brief History of our Number System Coming up in Series 3 Series Summary Exponents “I can’t change the direction of the wind, but I can adjust my sails to always reach my destination.”

Jimmy Dean

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SERIES ONE

A Paradigm Shift – Our Numbering System To best understand digitalization, one needs some knowledge of our numbering system.

What is it? What is its role in today’s digital technologies?

In simple terms, a numbering system creates an approach to represent numbers using a set of symbols. For us, these symbols are (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9). But to computers, it’s only (0) and (1). In this Series, I want to ingrain into your mind the methods of using these symbols to create a number. Once formed, a person or machine interprets the number as having some value. Likewise, digital systems use their symbols to create their own applicable numbers but using only zeros and ones. It’s a simple paradigm shift.

And yes! For digital experts, this may be your question. What is his rationale for spending time on a number system instead of immediately digging into digital waveforms, bits, and bytes? My answer is simple. I want to take a numbering system, which is familiar to everyone, show the nuts and bolts, and transfer the knowledge to new systems.

There are infinite amounts of numbering systems, but the one most familiar to us is known as the decimal system (in mathematical terms, it is called the Base-10 system). We use it in our everyday life without ever thinking about it.

However, to troubleshoot and work with digital systems, one has to have a working knowledge of decimal, binary, octal, and hexadecimal. I will show you the easiest way to navigate between them. I will begin with the decimal system, and then leverage the parallels and our learning of decimal into binary, octal, and hexadecimal. So let’s get started.

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The Decimal System

The next time you visit the gas station to refuel, take a look at the surface meters. Notice that the meters run counting from zero to nine. Interesting! Could the pump station have counted in any other sequences? Why not? Just stay tuned to learn.

Note! Understanding the decimal system may appear uninteresting. Why? It is the system that you have used in your everyday life without having to understand the dynamics of it. However, here’s what I want you to know; if you fully understand the principles of the decimal system, the others will be a breeze.

“In a decimal system, just remember groups of ten.”

So what in the world is the decimal system? Well, it equates to a numbering system consisting of ten digits from 0 to 9 (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). One can best remember it by thinking of it in terms of groups of ten.

Groups of ten! In Figure 1 Part A, a quick count discloses (30) rods. The big question is why (30)? Could it be another number? How did we derive at a (3) and a (0)? Thinking ha! Yes I know; for most, your answer is, “I just count it.” Yes, you did, but it was your counting skills driving the process. Knowing the mechanics behind the number process is a mute conversation. But for this lesson, it matters.

Take a look at Figure 1 Part B. I organize the rods in groups of ten. The result derives as three (3) groups of ten and zero (0) remaining, and therefore, I derive the number of 30.

Figure 1 Part A: Count of 30 rods

The process of grouping in tens Three (3) groups of ten and zero (0) remaining Creating the number of 30.

Figure 1 Part B: Example of Decimal System Makeup

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Okay good! Now let’s look at another example in Figure 2. The layout shows two groups of ten and four remaining, and therefore, we derive the number as 24 rods.

Recalling your first grade Math lessons, we also considered the number as (2) tens and (4) ones. Yes. We were just in tens. Wow!

|||||||||| |||||||||| ||||

2 Group of ten Two (2) groups of ten and 4 Remain The process of grouping in tens Four (4) remaining

Result of 24

Creating the number of 24.

Figure 2: Example of Decimal System Make

Simple Addition in the Decimal System

Let’s dig a little further. Figure 3 gives a brief explanation of adding two numbers. The example shows the process of adding (8) and (7) to derive at (15). Adhering to our lesson on the decimal system concept, we group the apples in tens resulting in one (1) group of ten and a remaining of five (5) apple. Hence, we recognize the number as (15).

Remember, the decimal system operates on groups of ten: the Base-10 System.

8 + 7 15

1 Group of Ten

5 Remain

Figure 3: Addition in a Decimal System Page 8

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Brief History of our Number System Our knowledge on the decimal numbering system so far may provide a clearer path to our understanding on other systems of importance for digitalization. We learned that the decimal system simply creates numbers by grouping in tens. But as a matter of concept, we can group in any numbering count. Today, the world accepts the decimal system as its acceptable system for counting and mathematics.

The Hindu-Arab developed the decimal system as a representation of the ten finger counting. Yes, indeed! We have ten fingers, and therefore the decimal system (Base 10) was easily adaptable.

In this publication, we will primarily focus on binary (Base-2), octal (Base-8), and hexadecimal (Base-16). In fact, octal and hex represent a compressed form of binary. However, just for argument sake, we can group in any numbering count. In Figure 4, I have compiled the results of 8 apples and its interpretation using other systems. Here it goes!

Numbering System Base 10 Base 8 Base 6 Base 5 Base 4 Base 2

Result 8

Group Grouping in tens

10 12 13 20 1000

Grouping in eights Grouping in sixes Grouping in fives Grouping in fours Grouping in twos

Figure 4: Result of 8 in

Yes, I know. Are you confused? No problem! Looking at the table at Base-5, for example, it automatically means that we are grouping in fives. Therefore, we have one (1) group of five and three (3) remaining. Hence, we conclude with an answer of 13.

Quite a change in thinking and seeing numbers. Right! It’s the paradigm shift. I do not want you to start pounding your head in the sand. So read it over.

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FUNNY BUT TRUE

The Mayan and other Mesoamerican cultures used a number system based on Base-20.

The ancient Babylonians used a Base-60 system.

Coming up in Series 3

But while the real world works in a decimal system, digital electronics operate in a binary (Base 2) environment. Why? The electronics applications rely on electricity, which consists of two states: ON and OFF. And only a binary can replicate a two-state system.

In Series 3, we will explore the binary system as well as octal and hexadecimal (hex) in digital technologies. These number systems make the world of digitalization not only possible but practical. They are the backbone of our modern computerized world.

SERIES SUMMARY A numbering system creates an approach to representing numbers using a set of symbols.

The world uses the decimal system for its counting and mathematical calculations.

The decimal system is also called the Base-10 system, which is a concept based on grouping in tens.

The decimal system consists of ten digits from 0 to 9 (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).

Digital systems cannot operate in a Base-10 system. It only works in a Base-2 system, which is known as binary.

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MATHEMATICS FOR GROWN FOLKS

2

3

Remembering EXPONENTS Exponent Base

61 42 73 104 28

6 to the first power 4 to the second power 7 to the third power 10 to the fourth power 2 to the power of eight

61 = 6 = 6 2 4 = 4 x 4 = 16 3 7 = 7 x 7 x 7 = 342 3 = 8 2 = 2 x 2 x 2 4 5 = 5 x 5 x 5 x 5 = 625 62 = 6 x 6 = 36 3 10 = 10 x 10 x10 = 1000 203 = 20 x 20 x 20 = 8000 28 = 2x2x2x2x2x2x2x2 = 256

PRACTICE EXPONENTS

5 =

3 6 = 82 = 25 =

4 3 = 02 =

0 12 =

2

ANSWERS

= = = = = = =

25 | 216 | 64 | 32 | 81 | 0 | 1

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A TRAINED WORKFORCE

I TRAIN(ForAND DEVELOP PEOPLE more information, see the back page)

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NOTES

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A TRAINED WORKFORCE

“A company with a robust training program converts good employees into great ones. By investing in their continued knowledge of your product and services, you are ensuring a greater likelihood of your employee delivering the best of a company’s offering with each customer interaction.” Attorney Latania Mena A trained workforce has long been a mark of distinction for the superiority of a successful business.

Employees are the frontline leaders for a business similar to soldiers first in line for battle. Whether dealing directly with the customer, producing the goods, or delivering the services, they are the most important representative of the business. The quality of the employee interactions and production solidly translate to the success of the business.

If you don’t believe, try the alternatives: bitchy employees, daunting processes, and intimidating supervisors.

These are tantamount to high turnover rate, low-value products, and services that suck -- the signature of hidden high expenses. Customers move to competitors resulting in loss of revenues and eventually business shutdown. Now, ask yourself, “Is training and development a good trade-off?”

In the current climate, many employers find the training and development of their workforce expensive. In fact, they budget little on training. Now think about it. A trained workforce has long been a mark of distinction for the superiority of a successful business.

• • • • • •

Compare the significant benefits to the marginal costs.

Build strength within the organization.

Address workforce weaknesses.

Ensure consistency and compliance.

Reduce customer complaints and return goods.

Increase accuracy as well as productivity.

Develop the quality brand standards.

• • • • • •

Increase innovation and creativity.

Cut employee turnover.

Enhance company brand.

Improve employee performance.

Improve employee satisfaction and morale.

Result in happy people.

Today, technologies are ingrained into our lives; it’s just the era that we live in. It changes so fast that continuous training must be part of the job to keep up. I design these series in Digital Electronics to help grown folks who see digital a threat to their livelihood. Others can benefit as a refresher or new information.

Email your questions; Ask me anything about DIGITAL ELECTRONICS sylvanus.donaie@gmail.com I TRAIN AND DEVELOP PEOPLE