Numeral Systems

Here are three kinds of counters. All three count the number of circles in the right panel. Click the green + and - buttons to add or remove circles.

The decimal counter has three wheels, each one with the digits: 0, 1, 2 ,3, 4, 5, 6, 7, 8, 9 written on it (see picture below). Every time you click +, the first (right) wheel advances to the next digit: from 0 to 1, then from 1 to 2, etc. When the first wheel completes a whole round and returns to 0, the second wheel advances to the next digit, and so on.

The binary counter works exactly in the same way, except one tiny difference. It has only two digits on each wheel: 0 and 1. If you click + twice, already the first wheel completes a whole round. Still, this counter is just as good as the decimal one, because if you know how to read it properly, you can figure out how many circles there are in the right panel. Computers use binary counters, because it is easy to represent the digits 0 and 1 using electric wires: if the current is switched on it represents the digit 1, and if it is off, it represents 0 (See an example in Logic gates).

The hexadecimal counter has not only the usual 0-9 digits on each wheel, but also six additional letters: A, B, C, D, E, F, making a total of 16 symbols. Like the binary and the decimal counters, the hexadecimal one is a perfectly good counter, once you get used to it. Computer programmers use it quite often, because it is easily translated to binary. See for yourself: click + until you complete a row of circles. Every time there is a full row, the first digit of the hexadecimal counter will be 0, as well as the first four digits of the binary counter.

See also

Proof that computers can't do everything

Demonstration of Compression

A book about computers for ages 9+

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