This Demonstration shows how binary numbers work. The number of digits varies between 2 and 8 and therefore the maximum numbers are (that is, 3, 7, 15, 31, 63, 127, 255). Because 0 is possible, there are numbers (that is, 4, 8, 16, 32, 64, 128, 256).
The binary numbers to be read in the upper graph are represented with the lowest bit at the bottom and the lower graph represents them in a traditional way from highest to lowest bit, bit number 0 being on the right.