Example 1: The Adder Circuit

In most computers there is a circuit called an adder . Its function is to take representations of two addends and produce a representation of their sum. In most computers today, each of these representations is stored in a series of circuits called a register . Think of a register as a storage medium for a single representation. The register is made up of a series of "bistable circuits"—circuits with two stable states, which we may conventionally label 0 and 1, being careful to remember that the numerals are simply being used as the labels of states, and are not the states themselves. (Nor do they represent the numbers zero and one.) The states themselves are generally voltage levels across output leads, but any physical implementation that has the same on-off properties would function equivalently. The adder circuit is so designed that the pattern that is formed in the output register is a func-

tion of the patterns found in the two input registers. More specifically, the circuit is designed so that, under the right interpretive conventions, the pattern formed in the output register has an interpretation that corresponds to the sum of the numbers you get by interpreting the patterns in the input registers.