First thing I wrote was “Analog is like grayscale.” I immediately erased it. Even the word “grayscale” is too technical for what I want to explain.

Remember Scantron? You used to have to bring a #2 pencil to take the test. You’d fill in bubbles A, B, C, D (or E: none of the above) to designate your answer.

Why #2? Because anything lighter might not register as a filled-in bubble. Anything darker might still register—even after you’ve erased it. Know what that process is called? Of taking various shades of graphite and making an all-or-nothing decision on them? It’s called Digitization.

There’s no doubt about it: the world is analog. Shades of gray occur all the time. So, why don’t computers operate on shades of gray? It takes longer to resolve and it’s not as repeatable. Computers (& all digital electronics) are based on a philosophy of doing extremely simple things very fast, very reliably.

Our brains, on the other hand, are built to allow for very complex connections that take time to resolve. And may resolve differently each time.

Once that Scantron machine has all our answers stored digitally, it can do a lot of amazing things. It can make identical copies of our multiple-choice selections. It can tally how everyone who was born on a Tuesday answered question # 123. (Turns out people born on a Tuesday are smarter.)

Why? (The Scantron operations, not the smart people born on Tuesday) Because these operations can be broken down into simple manipulations of 1’s and 0’s. You either got the question right or you didn’t. There’s no partial credit. Even if you filled in A 25% and D 75%, it makes a hard decision and picks one for you.

The building blocks of digital electronics are made to go fast and get the same answer every time. They’re also very small. I mean tiny. I mean that the width of my hair can handle a heck of a lot of these building blocks. So, when I put them all together, I end up with something that’s way more complicated. And powerful.

So, in the past, you might have had to answer 10 questions on a test. It might be a word problem. It might ask you about trains headed for each other. You might get partial credit if you wrote down the right equation but solved it wrong.

With Scantron, you don’t just get 10 problems. You get like 100. Since the computer can’t give you partial credit, it just asks you a lot of questions. If you know you’re stuff, you’ll likely get more of them right. It’ll be a pretty good approximation to getting partial credit.

So, the philosophy with digital electronics is to do many, many small crude 1 or 0 measurements, rather than a few precise measurements. Each individual measurement isn’t as important. What’s important is that we can store and process these measurements quickly reliably.

So, rather than map out a detailed tutorial, I am going to start posting some random thoughts and comparison that illustrate in some way the difference between analog and digital (and other technology concepts). They will be less polished, but hopefully, less formal.

1. More Channels
2. All or Nothing Reception
3. Deeper Coverage

More Channels

While analog TV has channels such as 2, 5, 7, 9, digital TV has 2.1, 2.2, 2.3; 5.1, 5.2, 5.3; 7.1, 7.2, 7.3; and 9.1, 9.2, 9.3. Digital signaling can reliably pack more information (and distinguish the sub-channels) than analog signaling. As a result, instead of broadcasting just one stream, there can be 3 streams—essentially 3 independent channels running on the same frequency.

It should be noted that analog channels refer to specific frequencies. For example, channel 2 is the lowest frequency in the TV band (from 54 MHz to 60 MHz). However, the wise professionals deciding standards for ATSC (that’s the digital TV standard in the US) decided that it would confuse people if all their favorite stations switched numbers all of a sudden—especially while they were told they needed to buy a new converter box to receive TV that they’ve been watching for over 60 years. At the same time, digital TV is being phased in side-by-side with analog TV. So, they couldn’t just turn off the analog channels and give them to the digital channels.

So, they came up with a scheme to allow channel numbers to remain the same: basically, the channel number has been separated from the frequency it is transmitted on. So, for example, in the Chicago area, digital channel 7.1 is transmitted from 698 MHz to 704 MHz—the equivalent of analog channel 52. This confuses me, since I thought channel 52 went up for auction recently. If anyone cares knows the answer, post it in the comments. Your TV is smart enough to display channel 7.1 regardless of which frequency it’s listening to.

All or Nothing Reception

I don’t want to panic anyone, but digital TV will be all or nothing in terms of your ability to receive it.

In the analog days, when things were bad, you’d see a fuzzy or snowy picture, but you’d see something. This is because your TV simply received the signal over the air and put it on your screen. The electron gun just did whatever the antenna said to do—without interpretation.

Now, your digital TV (or the digital converter box next to your analog TV) does a lot of interpreting. It makes millions of judgement calls a second, taking the signal it receives from your antenna and deciding if it’s a 1 or a 0. When things are good, the judgement is right close to 100% of the time and you get a perfect replica of what the station is broadcasting (with no degradation whatsoever).

However, when things are bad, the judgement calls that your TV (or converter box) makes get worse. Instead of putting a 0 out, it might put out a 1, and vice versa—flipping bits at random. If a large enough percentage of these 1’s and 0’s are flipped, the TV can’t make heads or tails of the signal (pun intended) and you basically get nothing.

The digital TV signal is compressed at the broadcaster in exactly the same way that your CD (which takes up 660 MB of space) can be squeezed down to 10 MP3’s (taking up around 30 MB of space) by removing artifacts that most can’t hear.  In fact, the term MP3 means MPEG layer 3. MPEG is the Motion Picture Experts Group, which defined the compression for video (including DVD’s and digital TV). Audio MP3’s merely inherited the benefit of their work. When your TV receives the signal, it needs to decompress it. If enough of the bits are wrong, the digital stream looks nothing like a compressed video to the MPEG decoder. So, the MPEG decoder gives up and shows nothing.

Deeper Coverage

This last expectation—deeper coverage—is merely my expectation. It is basically based on the idea that the analog TV that we receive now is approximately 60 years old. As a result, sophisticated processing techniques (digital signal processing being the most notable) weren’t available to the designers of the analog TV standard. However, we have gained 60 years of research. As a result, starting with a new standard means more advanced reception techniques built into the standard. Such things as forward error correction should make the signal more resilient for more people.

These advanced techniques are already built into the digital TV standard. There’s little much you or I can do along the lines of digital signal processing to improve your picture quality with digital TV. However, all the old analog techniques of boosting power and minimizing noise still apply. At home, you can still use these techniques so that you can fall into the All rather than the Nothing category. I’ll post my advice for maximizing your signal quality (if you live on the fringe) sometime soon.

Nothing

The best way to explain how computers count is to show an example. Let’s review again the way we count.

Three versions of 3

When someone shows three fingers to us (with one finger and a thumb folded down), we interpret the number three:

However, there are more ways of representing the same number:

The reason is that we assign the same value to each finger. Any three fingers being up signifies the number three.

All fingers are not created equal

The analogous counting system with computers is to assign different values to each finger. Look closely at the following picture (click on it if you have to). You’ll notice the numbers eight, four, two, and one on the fingers:

Illustration 1

When we see a hand with fingers up, we add up the numbers on the finger. Some examples:

Illustration A: The number fourteen (8+4+2)

Illustration B: The number seven (4+2+1)

Illustration C: The number nine (8+1)

Putting it in numbers

So, here’s how computers represent each number above: They assign a 1 or a 0 to each finger position. If the finger is up, it’s assigned a 1. If the finger is down, it’s assigned a 0.

So example A (fourteen) would be represented as 1110. Example B above (five) would be represented as 0111. Example C would be represented as 1001.

Incidentally, the weighting of 8, 4, 2, 1 on each finger is called binary weighting: each finger has a value of twice the finger to the right of it. To complete the analogy, each finger represents one bit: one unit of binary information (a 1 or a 0). With four fingers/bits, we can represent any number between zero (all fingers down) to fifteen (Illustration A: all fingers up; 8+4+2+1).

A big part of this processing is the ability to represent anything in a binary format. My definition of binary is a representation which only involves two states (or combinations of these two states).

This definition is rather terse. I’ll attempt to illustrate it in the next two posts. However, before we dive into binary, let’s review something that is almost so intrinsic to our thinking about numbers that we take it for granted:the decimal system. Our first step into understanding the decimal system will be to contrast it with the roman numeral system.

Roman Numerals

Most of us are familiar with the roman numeral system. If one were to count using Roman numerals, it would look like this:

I
II
III
IV
V
VI
VII
VIII
IX
X
XI
XII
XIII
XIV
XV
XVI

Basically, I, V, X, etc are unit values. Learning Roman Numerals is akin to learning how to count change: there’s no regular pattern. There’s a penny (I), a nickel (V), and a dime (X). You have to break down any number into these units. In fact, it’s even worse than counting change: the numeral IX means “a dime minus a penny”.

The problem with Roman numerals is that they are very irregular. There’s no pattern to build off of. (Actually, there’s a pattern enough to program a computer to do it, but it’s not as simple as it could be.) Representing 9 (IX) is very different than representing 9000 (MMMMMMMMM).

Arabic Numerals

When I say the decimal system, I don’t mean the system of using meters (metres), millimeters (millimetres), etc. Instead, I mean our system of counting. When we need to represent a number, we all pull out the decimal system without realizing.

In reality, all numbers are really ideas that have a representation. For example, there’s the notion of nine apples. I can represent that by writing 9 apples or IX apples. It is exactly the same as writing cat or gato or chat.

Fortunately/Unfortunately, unlike the cat/gato/chat, which has different representations, almost all of the globe represents the number nine the same way: the Arabic numeral “9”.

The Arabic Numerals are the numerals 0,1,2,3,4,5,6,7,8,9. Using this small alphabet of numerals, we can practically represent any number in the world.

Let’s contrast our method of counting by creating a table between Roman and Arabic numerals:

Roman Numeral	Arabic Numeral
I	1
II	2
III	3
IV	4
V	5
VI	6
VII	7
VIII	8
IX	9
X	?
XI	?
XII	?
XIII	?
XIV	?
XV	?

Unfortunately, the number ten has no Arabic Numeral representation; the numerals stop at 9. So, what do we do? Well, we add another digit: we create another space for numbers to the left of our original numbers and then start over at 0. I’ll show this extra digit in maroon.

Roman Numeral	Decimal Representation
I	1
II	2
III	3
IV	4
V	5
VI	6
VII	7
VIII	8
IX	9
X	10
XI	11
XII	12
XIII	13
XIV	14
XV	15

Here’s what we did: We added another set of digits to the left of our previous set and started counting over from 0. It’s tempting to see the notation “14″ and call it fourteen. However, when discussing number system, it’s better to call it “one-four”. The reason is that “14″ is our best way of representing fourteen, but there are other ways. This post (and the next) attempts to detach numbers from the many ways of representing them.

The reason that we ended up with the decimal number system is that we have ten fingers: we can actually count from one to ten. Notice that there are ten Arabic numerals: 0,1,2,3,4,5,6,7,8,9–the same as the number of fingers we have, even though they don’t exactly correspond to how we count on fingers (one, two, three, four, five, six, seven, eight, nine, ten).

Generally, humans tend to count with one rather than zero. However, in numbering systems it’s better to start with 0. The reason is that when we reach 9, we add another digit (1) and reset the second digit to 0–getting 10. (Alternatively, we can just remember that after 9, we wrap back around to 0.)

In the next post, I will explain how computers count with only two fingers.

The electronic industry has been and will forever be reducing cost and adding features. As a result, more complexity is being required of electronic devices while reducing the cost of these devices.

The complexity translates itself into more functional blocks being placed into the devices:

Analog processing

Unfortunately, every analog device suffers from three problems:

noise
distortion
variation

noise is the random variations in current and voltage. Suppressing noise requires increasing the circuit’s size and/or power consumption.

distortion is the deviation of an analog function from its ideal

variation is the fact that one cannot make two analog circuits exactly the same. There are always manufacturing variations that cause each circuit to have different characteristics.

Digital processing

Digital processors do not suffer from the above problems. They instead work on sequential values, are able to compute functions of these values exactly, and store or output the results.

If one asks a digital circuit to compute y=x^2+3.141, it can be designed to give as exact a result as one wants. The only way the digital circuit can make an error is if it assigns a value of 0 rather than 1 to some bit somewhere.

Rounding

There is one feature of digital circuits that I haven’t discussed yet: the notion of rounding.

I’ll explain in a future post how bits of 0 and 1 can represent arbitrary numeric values. Until then, just take my word that the only way a digital circuit can mess up is by generating a 0 when it should have generated 1 or vice versa.

When an analog signal is being converted to digital, its value is both sampled and rounded. The reason is that all digital circuits have finite precision. There are only so many bits that can fit—and only so many bits are worth fitting.

It’s very unlikely that the average July temperature measured at Chicago O’Hare airport is exactly 84 degrees. It’s probably something like 84.3 degrees. However, that last 0.3 degree is not going to make you pick a black sweater over a light T-shirt. Let’s round it to 84 degrees. There is some error, but it is rather insignificant.

In almost all cases, the rounding error caused by this quantization can be made lower than the noise and distortion an equivalent analog circuit would inject.

In fact, it is due to this rounding that variation is not such an issue with digital circuits. One can provide enough margin so that variation is not enough to create a bit error—and the only way a digital circuit can make a mistake is if it stores or sends out the wrong bit value.

The aDa line-up

Whereas in the past, one would have functional blocks A,B,C,D all analog, one now has the following system:

The functions A, B, C, and D are all implemented digitally. The blocks y and z convert from analog to digital (analog-to-digital converter—ADC) and from digital to analog (digital-to-analog converter—DAC). The overhead of the added analog blocks y and z is greatly outweighed by the saving in area and power (and the increase in functionality) afforded by making A, B, C, and D all digital.

In many cases, one wants the end result to be digital (for example, recording to a CD). So, the last stage need not exist. (Or it exists in the form of a laser that writes the bits to the disc.)

In other cases, the source is digital but the eventual output is analog—for example a CD player. In these cases, block y is not required. The CD player can do things such as equalization and surround sound processing all digitally.

In a future post, I’ll explain why those analog blocks y & z are necessary.

signal: a digital signal occurs as a sequence of values

gadget: a digital gadget processes information sequentially

From this definition, very few things that one encounters are intrinsically digital. Nonetheless, many analog signals are converted to digital (through a process called sampling or digitizing) and can gain the benefits of digital processing.

Signals

Very few intrinsically digital signals exist. Some notable ones are:

stock prices
votes (per hour) in an election
musical notation

In a free market, the market sets the stock price. As a result, there’s no price assigned to a stock unless a trade occurs. Consequently, stock prices are a sequence of values, not a continuum of values.

Note that intrinsically digital signals result from instantaneous events of events with well-defined start and stop times. (Start and stop times are instantaneous events.)

This very narrow definition of digital begs the question: how did digital processing over-take analog processing when most of what one encounters is analog?

The reason is that any analog signal can be converted to digital through a process called sampling.

Let’s look again at the temperature measured at Chicago O’Hare airport. One will notice that there are bubbles for each month. For each month, one can record the average temperature in that month. One has sampled the temperature once per month. So, one has taken an analog signal and converted to a sequence of values—one has converted it to a digital signal.

Although the temperature is analog, we have used a sequence of instantaneous events (sampling once per month) to convert it into a digital signal.

While one loses some amount of information in converting from analog to digital, one can see that there’s not a heck of a lot happening in-between June and July that connecting the dots from 79 degrees to 84 degrees wouldn’t show:

Gadgets

Consider the digital watch. Some of you may have watches that look like an analog watch—possibly with three hands (hour, minute, seconds) rather than two (hour, minute). If you have one of these, take a close look at the seconds hand. You’ll notice that it makes jumps, hopping from one number to the next.

Inside the watch, there is a digital circuit that updates the time every second—it processes the time update as a sequence of values.

Consider the compact disc—a digital recording device, in contrast to the analog cassette tape.

To get a recording on CD, the sound wave goes into the microphone and is converted to a voltage. Somewhere (inside your computer for example), an analog-to-digital converter measures the voltage periodically. This sampling needs to be done frequently enough so that we don’t give the signal much time in-between samples to do anything other than connect the dots:

infrequent sampling

frequent sampling

In the case of CD’s, the sound is sampled at a rate of 44,100 times per second, or 44.1 kHz. Note that this is a bit more than twice the generally accepted highest frequency of sound: 20 kHz.

signal: an analog signal is a signal that always has a value. They key term is always.

gadget: an analog gadget operates continuously on an analog signal.

By this definition, everything that occurs naturally is analog. This property of natural phenomena occurs because almost all physical laws are continuous—they define a relationship between signals that is true always. They don’t define a relationship between a sequence of values.

Analog Signals

Consider a runner’s distance from the starting line. Distance is an analog signal. A runner cannot start at the starting line and end at the finish line without being somewhere in-between during the race. Runners don’t simply disappear and re-appear elsewhere.

One can graph the runner’s distance from start to finish in a smooth manner—without lifting one’s pen off the paper:

Similarly, looking back at temperature measured at Chicago O’Hare airport, one can see that the temperature doesn’t make a step jump from 79 degrees in June to 84 degrees in July. It moves smoothly from one temperature to the other.

Analog Gadgets

Consider an analog watch. The analog watch gets wound up, and its little gears move smoothly. They don’t update the time ever second. They are constantly moving. The position of the hands on the watch don’t jump from point to point. They move smoothly from point to point.

Similarly, consider an analog recording: audio cassettes. A microphone picks up sound pressure and converts it to a current. The current is then passed to the tape recorder. The tape recorder generates a magnetic field proportional to the current (and therefore proportional to sound pressure), resulting in a recorded magnetic configuration on the tape.

Note that all this information transfer occurs continuously. The sound just flows to the microphone, producing an electrical current that flows to the magnetic medium which then impinges a magnetic field into the tape.

Nonetheless, most people don’t know what the word digital means. In this multi-part series, I will explain the difference between digital and analog, why digital processing is better than analog, and why some analog processing will never go away.

The words analog and digital are both adjectives. What types of nouns do they generally modify?

signals
gadgets

A signal is anything that has a numeric value that varies with time.

So, for example, naturally occurring things such as:

temperature
volume
pressure
voltage
current
force / torque
distance/speed/acceleration
angle/angular speed/angular acceleration
light intensity

are all signals.

Each of these things varies with time. For example, the temperature measured at Chicago O’Hare airport varies both with the hour of the day and with the day of the year.

In addition, several artificial constructions are also signals:

stock prices
votes (per hour) in an election
traffic rates on the Internet

Gadgets are what you think they are—electronic devices, but also appliances, machines, etc.

Examples of gadgets are:

watches
thermometers
telephones
audio recorder/players
video recorder/players

Engineers and mathematicians refer to gadgets (or their component building-blocks) as systems.

It should be noted that a gadget being analog or digital comes down to whether it processes analog signals or digital signals.

In the next post, I’ll explain the characteristics of analog signals and gadgets. In a future post, I will explain characteristics of digital signals and gadgets.