Binary numbers

A light switch only knows on and off, and yet with five switches you can already count to 31. Every computer works exactly like that: deep inside there are only two states, current on and current off. From these two states it builds numbers, texts, photos, and entire games. Here you will see how that works with numbers.

Place values: 1, 2, 4, 8, 16

In the decimal system, the places are worth 1, 10, 100: each place is worth ten times the one to its right. In the binary system there are only the digits 0 and 1, so each place is worth twice the one to its right instead of ten times as much: 1, 2, 4, 8, 16 and so on, read from the right. A 1 means: this place value counts. A 0 means: it does not. So the binary number 101 means 4 + 0 + 1, which is 5.

From binary to decimal and back

Binary to decimal is pure adding: write its value under each place and add all values that have a 1. For the way back, first look for the largest place value that still fits into your number, then work down through the smaller ones. For 11 that is 8, because 16 would already be too big. Does 8 fit? Yes, write a 1, and 3 are left over. Does 4 fit? No, write a 0. Does 2 fit? Yes, another 1, and 1 is left over. Does 1 fit? Yes, one more 1. Result: 1011.

Counting with 0 and 1

Counting works in binary just like in the decimal system, except the carry comes much earlier: 0, 1, and the place is already full. It continues with 10, 11, 100, 101, 110, 111. Whenever all places show 1, the next step flips everything to 0 and a new 1 appears on the left, exactly like 99 + 1 = 100.