Powers of Two

Powers of two are the doubling numbers –
2, 4, 8, 16, 32 ...

They can be calculated as –
2, 2 × 2, 2 × 2 × 2, 2 × 2 × 2 × 2, 2 × 2 × 2 × 2 × 2 ...
– which can be written more simply as –
21, 22, 23, 24, 25...

If you fold a sheet of paper in half and fold it again and again, each fold will double the number of thicknesses of paper. One fold produces two layers, two folds make four layers, and so on, going up in powers of two.

There is a famous legend about a Persian king who wanted to reward the man who invented the game of chess. When asked what he wanted, the man pointed to the chessboard. He asked for a single grain of wheat on the first square of the board, two grains of wheat on the second square, four grains on the third square, and so on in powers of two, up to the 64th square. This sounds quite a reasonable request, but if the king had agreed to it, he would have needed 9,223,372,036,854,775,808 grains for the 64th square, which is more than the world's annual wheat harvest today.

See also powers.

Based on the book Numbers: Facts, Figures & Fiction.