How can just 0 and 1 write every number and every letter?

With two symbols you can write anything, as long as you let their position carry meaning. In binary, each digit, called a bit, is worth a power of 2: from the right, 1, 2, 4, 8, 16 and so on. A number's value is simply the sum of the places that hold a 1. So 1101 means 8 + 4 + 1, which is 13. Counting works just like ordinary counting with fewer symbols: 0, 1, then you run out, so you reset to 0 and carry a 1 to the left, giving 10, 11, 100.

Letters are just numbers with a name tag. In the ASCII code, every character gets a number from 0 to 127, and the lowercase letter a is 97, stored as 1100001. Computers love this because two states are easy to build and hard to confuse: a switch on or off, two different voltages, two magnetic directions on a disk. Noise can blur a signal a little without turning one state into the other.

The idea is much older than electronics. In 1605 Francis Bacon described turning letters into strings of two symbols, hidden as tiny differences in a font, and noted that bells, trumpets, torches or musket shots would do just as well. The philosopher Gottfried Leibniz filled more than a hundred manuscripts with binary, and saw in 0 and 1 a symbol of creation out of nothing.