Chapter 10 - Gating and Logic Circuits

Abstract

Logic circuits exist to carry out a set of logic actions such as are used for controls for washing machines, tape-recorder drives, computer disk drives, security systems, and a host of industrial control actions. Simple arithmetic actions can also be carried out using logic circuits. All logic actions, however complicated, can be analyzed into simple actions that are called AND, OR, and NOT, so that circuits, called gates, which carry out such actions, are the basis of logical circuits. Any gate circuit can be analyzed by drawing up a truth table, or a set of truth tables. A truth table is a simple way of showing what the output of a gate or gate circuit will be for each and every possible combination of inputs. The alternative is to use Boolean algebra, a process that is greatly simplified by computer programs that carry out an analysis of gate circuits. The Boolean algebra alternative method relies on using lettering to identify all inputs, outputs, and intermediate points, and drawing up the truth table in stages, starting with all possible combinations at the inputs. An arithmetic circuit is a set of gates with a separate set of inputs for each number that has to be processed. The gates are connected to carry out an arithmetic action and the outputs of the gate circuit are the digits of the result (addition, subtraction, multiplication, or division). Encoders, decoders, multiplexers, and demultiplexers are used to change the way that digital codes are carried.