## How does a computer count to 1,024?

Remember a while back I talked about what your garage door opener had in common with Internet addressing.

Let’s take it a step further.

As you recall we said that your attache case or luggage carrier had a three wheel combination lock (click on the picture for a closer view).

Let’s take this one step further: let’s dial the combination “137.”

What this means is that the “1″ has been dialed on the “100’s” wheel, the “3″ has been dialed on the “10’s” wheel and the “7″ has been dialed on the “1’s” wheel.

This is the same as saying 100 + 30 + 7 = 137

Please note: 10 the the second power is what we call the “100’s” wheel, 10 to the first power is what we call the “10’s” wheel, and
10 to the zero power is what we call the “1’s” wheel.

Let’s also notice that since each wheel has 10 possible numbers (0-9), then we are working with a base-10 sytstem. And since we have 3 wheels, we can calculate the total number of combinations by calculating the value of 10 cubed, or 10 to the 3rd power, which equals 1,000 different combinations.

How about those dip switches inside your garage door opener?

Well, first of all, each switch can only have one of two values (”on-off”), so we call it a base-two system (or “binary”).

Click the picture on the left to get a close-up of the dip switch. See how the individual switches are labeled #1 - #10, left to right? Let’s set them like this and figure out what the combination is on your garage door opener:

#1 = up (on, or “1″)
#2 = down (off, or “0″)
#3 = on (”1″)
#4 = off (”0″)
#5 = on (”1″)
#6 = off (”0″)
#7 = on (”1″)
#8 = off (”0″)
#9 = on (”1″)
#10 = off (”0″)

If we read left to right, we get this combination:

1010101010

That is the base-two (binary) combination for your garage door opener. And it is a 10-bit number.

What is the maximum number of combinations? 2 to the 10th power or 1,024 combinations.

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