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Most of the terms shown here are informal, and have not been made "authoritative" by any standards group or other sanctioning body. However, their inclusion into this chapter is warranted by their occasional appearance in technical literature, as well as the levity they add to an otherwise dry subject: • Bit: A single, bivalent unit of binary notation. " • Crumb, Tydbit, or Tayste: Two bits. • Nibble, or Nybble: Four bits. • Nickle: Five bits. • Byte: Eight bits. • Deckle: Ten bits. • Playte: Sixteen bits.
There is no such thing as "2" or "-1" or "1/2" in the Boolean world. It is a world in which all other possibilities are invalid by fiat. As one might guess, this is not the kind of math you want to use when balancing a checkbook or calculating current through a resistor. However, Claude Shannon of MIT fame recognized how Boolean algebra could be applied to on-and-off circuits, where all signals are characterized as either "high" (1) or "low" (0). His 1938 thesis, titled A Symbolic Analysis of Relay and Switching Circuits, put Boole's theoretical work to use in a way Boole never could have imagined, giving us a powerful mathematical tool for designing and analyzing digital circuits.
We did this to emphasize an important but easily neglected aspect of DeMorgan's theorem. Since a long bar functions as a grouping symbol, the variables forl1lerly grouped by a broken bar must remain grouped lest proper precedence (order of operation) be lost. In this example, it really wouldn't matter if we forgot to put parentheses in after breaking the short bar, but in other cases it might. Consider this example, starting with a different expression. As you can see, maintaining the grouping implied by the complementation bars for this expression is crucial to obtaining the correct answer.