Binary Counting: Build a Number from Lamps

The sixth intro introduces binary notation through play: four lamps weighted 1, 2, 4 and 8, out of which you build a number. Here is the gist of the experiment and the rule.

Experiment: four lamps

Each lamp is either lit or dark; a lit lamp adds its weight to the total. Building 5 means turning on the "4" and "1" lamps: 4 + 1 = 5. The "2" and "8" lamps stay dark — they add nothing. There is no "5" lamp: the weights are only powers of two.

The rule: digits and the carry

A lamp number is written right to left: the rightmost digit is 1, then 2, 4 and 8. For example, 0101 is 4 + 1, which is 5. If all four lamps are lit, the notation 1111 means 8 + 4 + 2 + 1 = 15. Add one more: every lamp goes dark, the notation reads 0000, and the extra one falls off the edge — that is a carry.

Transfer: read the notation

Check yourself: what does 0110 mean? The "4" and "2" lamps are lit, so it is 6. Every number from 0 to 15 is built from the four lamps, and each set has exactly one notation.

Where it is used

Binary counting is the language of every digital device. Every number in a computer, every memory address and every pixel is a set of digit-lamps. And the carry that fell off the edge is the heart of the adder: it is how a processor sums any numbers.