World of Zeros and Ones I

We've looked at the number of possible combos we can get with a specific number of bits. How should we do the reverse operation and find the number of bits we need? It's simple algebra, actually: the number of combos = 2ⁿ, n = log₂(number of combos).

For example, there are eight planets in our solar system. To represent them all, we need log₂8 = 3 bits. The keying sequence for your calculator is LOG 8 ÷ LOG 2 (since log_an = log n / log a).

That example is simple enough, so let's move on to a more complex one. Let's say we need to represent all the bird species in the world, of which there are about 10,000. Then we'll need log₂10000 = 13.2877123... Hang on! Bits are discrete, so we can't have 0.2877123 of them! Well, the solution is always to round up, which means we'll need 14 bits.

The following script converts between the number of bits and the number of combos. Try entering large numbers into bits and watch as the combo number grows exponentially!