Silence on the Wire

Toward the Universal Operator

The path to simplicity often leads through a seemingly needless level of complexity—and this case is no exception. To even begin, we must consider the work of another 19th-century mathematician, Augustus DeMorgan (1806–71). DeMorgan’s law states that “a complement of disjunction is the conjunction of complements.” This infamous exercise in obfuscating trivial concepts has some profound consequences for Boolean logic and, ultimately, the design of digital circuits.

In plain English, DeMorgan’s law explains that when any (or both) of two conditions is not satisfied, a sentence that claims that both conditions are met (or, in other words, a conjunction of conditions occurs) will be false as well—oh, and vice versa.

The ...