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The problem is that we have a table that provides this translation:

Alphabetical letter → Morse code dots and dashes

But we don't have a table that lets us go backward:

Morse code dots and dashes → Alphabetical letter

In the early stages of learning Morse code, such a table would certainly be convenient. But it's not at all obvious how we could construct it. There's nothing in those dots and dashes that we can put into alphabetical order.

So let's forget about alphabetical order. Perhaps a better approach to organizing the codes might be to group them depending on how many dots and dashes they have. For example, a Morse code sequence that contains either one dot or one dash can represent only two letters, which are E and T:

A combination of exactly two dots or dashes gives us four more letters—I, A, N, and M:

A pattern of three dots or dashes gives us eight more letters:

And finally (if we want to stop this exercise before dealing with numbers and punctuation marks), sequences of four dots and dashes give us 16 more characters:

Taken together, these four tables contain 2 plus 4 plus 8 plus 16 codes for a total of 30 letters, 4 more than are needed for the 26 letters of the Latin alphabet. For this reason, you'll notice that 4 of the codes in the last table are for accented letters.

These four tables might help you translate with greater ease when someone is sending you Morse code. After you receive a code for a particular letter, you know how many dots and dashes it has, and you can at least go to the right table to look it up. Each table is organized so that you find the all-dots code in the upper left and the all-dashes code in the lower right.

Can you see a pattern in the size of the four tables? Notice that each table has twice as many codes as the table before it. This makes sense: Each table has all the codes in the previous table followed by a dot, and all the codes in the previous table followed by a dash.

We can summarize this interesting trend this way:

Number of Dots and Dashes

Number of Codes

1

2

2

4

3

8

4

16

Each of the four tables has twice as many codes as the table before it, so if the first table has 2 codes, the second table has 2 x 2 codes, and the third table has 2 x 2 x 2 codes. Here's another way to show that:

Number of Dots and Dashes

Number of Codes

1

2

2

2 x 2

3

2 x 2 x 2

4

2 x 2 x 2 x 2

Of course, once we have a number multiplied by itself, we can start using exponents to show powers. For example, 2 x 2 x 2 x 2 can be written as 24 (2 to the 4th power). The numbers 2, 4, 8, and 16 are all powers of 2 because you can calculate them by multiplying 2 by itself. So our summary can also be shown like this:

Number of Dots and Dashes

Number of Codes

1

2 1

2

2 2

3

2 3

4

2 4

This table has become very simple. The number of codes is simply 2 to the power of the number of dots and dashes. We might summarize the table data in this simple formula:

number of codes = 2number of dots and dashes

Powers of 2 tend to show up a lot in codes, and we'll see another example in the next chapter.

To make the process of decoding Morse code even easier, we might want to draw something like the big treelike table shown here.

This table shows the letters that result from each particular consecutive sequence of dots and dashes. To decode a particular sequence, follow the arrows from left to right. For example, suppose you want to know which letter corresponds to the code dot-dash-dot. Begin at the left and choose the dot; then continue moving right along the arrows and choose the dash and then another dot. The letter is R, shown next to the last dot.

If you think about it, constructing such a table was probably necessary for defining Morse code in the first place. First, it ensures that you don't make the dumb mistake of using the same code for two different letters! Second, you're assured of using all the possible codes without making the sequences of dots and dashes