Humans have always desired mechanical aids to computations. There is evidence of "computing" devices such as the present-day abacus, from as early as the thirteenth century C.E. The first computing devices were accumulators only capable of adding or subtracting. Even "adding machines," which were made well into the twentieth century, could only perform that one function. Subtraction is nothing more than adding a negative number.

Nearly all modern computers are digital, which means that all the internal machine states are either on or off, a one or a zero, true or false, or other nomenclature. There is nothing between a zero and a one such as one-half or one-third etc. The number of bits used to define a quantity sets the number of different values that the quantity can have. As an example, a quantity represented by an 8-bit binary number can only...