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Author Charles Petzold
Pages 400
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Level All Levels
Published 10/11/2000
ISBN 9780735611313
Price $17.99
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Chapter 9. Bit by Bit by Bit


When Tony Orlando requested in a 1973 song that his beloved "Tie a Yellow Ribbon Round the Ole Oak Tree," he wasn't asking for elaborate explanations or extended discussion. He didn't want any ifs, ands, or buts. Despite the complex feelings and emotional histories that would have been at play in the real-life situation the song was based on, all the man really wanted was a simple yes or no. He wanted a yellow ribbon tied around the tree to mean "Yes, even though you messed up big time and you've been in prison for three years, I still want you back with me under my roof." And he wanted the absence of a yellow ribbon to mean "Don't even think about stopping here."

These are two clear-cut, mutually exclusive alternatives. Tony Orlando did not sing, "Tie half of a yellow ribbon if you want to think about it for a while" or "Tie a blue ribbon if you don't love me anymore but you'd still like to be friends." Instead, he made it very, very simple.

Equally effective as the absence or presence of a yellow ribbon (but perhaps more awkward to put into verse) would be a choice of traffic signs in the front yard: Perhaps "Merge" or "Wrong Way."

Or a sign hung on the door: "Closed" or "Open."

Or a flashlight in the window, turned on or off.

You can choose from lots of ways to say yes or no if that's all you need to say. You don't need a sentence to say yes or no; you don't need a word, and you don't even need a letter. All you need is a bit, and by that I mean all you need is a 0 or a 1.

As we discovered in the previous chapter, there's nothing really all that special about the decimal number system that we normally use for counting. It's pretty clear that we base our number system on ten because that's the number of fingers we have. We could just as reasonably base our number system on eight (if we were cartoon characters) or four (if we were lobsters) or even two (if we were dolphins).

But there is something special about the binary number system. What's special about binary is that it's the simplest number system possible. There are only two binary digits—0 and 1. If we want something simpler than binary, we'll have to get rid of the 1, and then we'll be left with just a 0. We can't do much of anything with just a 0.

The word bit, coined to mean binary digit, is surely one of the loveliest words invented in connection with computers. Of course, the word has the normal meaning "a small portion, degree, or amount," and that normal meaning is perfect because a bit—one binary digit—is a very small quantity indeed.

Sometimes when a new word is invented, it also assumes a new meaning. That's certainly true in this case. A bit has a meaning beyond the binary digits used by dolphins for counting. In the computer age, the bit has come to be regarded as the basic building block of information.

Now that's a bold statement, and of course, bits aren't the only things that convey information. Letters and words and Morse code and Braille and decimal digits convey information as well. The thing about the bit is that it conveys very little information. A bit of information is the tiniest amount of information possible. Anything less than a bit is no information at all. But because a bit represents the smallest amount of information possible, more complex information can be conveyed with multiple bits.

By saying that a bit conveys a "small" amount of information, I surely don't mean that the information borders on the unimportant. Indeed, the yellow ribbon is a very important bit to the two people concerned with it. Another way to view information is as a choice or selection among two or more possibilities. When you speak a sentence, for example, your words are chosen from a whole dictionary of possible words. A single bit indicates a choice between just two possibilities (such as "stay away" or "come home"), and two is surely the smallest useful number of possibilities. Multiple bits indicate a choice between more than two possibilities. "Listen, my children, and you shall hear / Of the midnight ride of Paul Revere," wrote Henry Wadsworth Longfellow, and while he might not have been historically accurate when describing how Paul Revere alerted the American colonies that the British had invaded, he did provide a thought-provoking example of the use of bits to communicate important information:

He said to his friend "If the British march
By land or sea from the town to-night,
Hang a lantern aloft in the belfry arch
Of the North Church tower as a special light,—
One, if by land, and two, if by sea."

To summarize, Paul Revere's friend has two lanterns. If the British are invading by land, he will put just one lantern in the church tower. If the British are coming by sea, he will put both lanterns in the church tower.

However, Longfellow isn't explicitly mentioning all the possibilities. He left unspoken a third possibility, which is that the British aren't invading just yet. Longfellow implies that this possibility will be conveyed by the absence of lanterns in the church tower.

Let's assume that the two lanterns are actually permanent fixtures in the church tower. Normally they aren't lit:

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This means that the British aren't yet invading. If one of the lanterns is lit,

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or

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the British are coming by land. If both lanterns are lit,

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the British are coming by sea.

Each lantern is a bit. A lit lantern is a 1 bit and an unlit lantern is a 0 bit. Tony Orlando demonstrated to us that only one bit is necessary to convey one of two possibilities. If Paul Revere needed only to be alerted that the British were invading (and not where they were coming from), one lantern would have been sufficient. The lantern would have been lit for an invasion and unlit for another evening of peace.

Conveying one of three possibilities requires another lantern. Once that second lantern is present, however, the two bits allows communicating one of four possibilities:

00 = The British aren't invading tonight.

01 = They're coming by land.

10 = They're coming by land.

11 = They're coming by sea.

What Paul Revere did by sticking to just three possibilities was actually quite sophisticated. In the lingo of communications theory, he used redundancy to counteract the effect of noise. The word noise is used in communications theory to refer to anything that interferes with communication. Static on a telephone line is an obvious example of noise that interferes with a telephone communication. Communication over the telephone is usually successful, nevertheless, even in the presence of noise because spoken language is heavily redundant. We don't need to hear every syllable of every word in order to understand what's being said.

In the case of the lanterns in the church tower, noise can refer to the darkness of the night and the distance of Paul Revere from the tower, both of which might prevent him from distinguishing one lantern from the other. Here's the crucial passage in Longfellow's poem:

And lo! As he looks, on the belfry's height
A glimmer, and then a gleam of light!
He springs to the saddle, the bridle he turns,
But lingers and gazes, till full on his sight
A second lamp in the belfry burns!

It certainly doesn't sound as if Paul Revere was in a position to figure out exactly which one of the two lanterns was first lit.


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Last Updated: Friday, July 6, 2001