LOGIC DIAGRAMSLogic diagrams are used in the operation andmaintenance of digital computers. Graphic symbolsfrom ANSI Y32.14 are used in these diagrams.Computer LogicDigital computers are used to make logicdecisions about matters that can be decided logically.Some examples are when to perform an operation,what operation to perform, and which of severalmethods to follow. Digital computers never applyreason and think out an answer. They operate entirelyon instructions prepared by someone who has done thethinking and reduced the problem to a point wherelogical decisions can deliver the correct answer. Therules for the equations and manipulations used by acomputer often differ from the familiar rules andprocedures of everyday mathematics.People use many logical truths in everyday lifewithout realizing it. Most of the simple logicalpatterns are distinguished by words such as and, or,not, if, else, and then. Once the verbal reasoningprocess has been completed and results put intostatements, the basic laws of logic can be used toevaluate the process. Although simple logicoperations can be performed by manipulating verbalstatements, the structure of more complex relation-ships can more usefully be represented by symbols.Thus, the operations are expressed in what is knownas symbolic logic.The symbolic logic operations used in digitalcomputers are based on the investigations of GeorgeBoole, and the resulting algebraic system is calledBoolean algebra.The objective of using Boolean algebra in digitalcomputer study is to determine the truth value of thecombination of two or more statements. SinceBoolean algebra is based upon elements having twopossible stable states, it is quite useful in representingswitching circuits. A switching circuit can be in onlyone of two possible stable states at any given time;open or closed. These two states may be representedas 0 and 1 respectively. As the binary number systemconsists of only the symbols 0 and 1, we can see thesesymbols with Boolean algebra.In the mathematics with which you are familiar,there are four basic operations—addition, subtraction,multiplication, and division. Boolean algebra usesthree basic operations—AND, OR, and NOT. If thesewords do not sound mathematical, it is only becauselogic began with words, and not until much later wasit translated into mathematical terms. The basicoperations are represented in logical equations by thesymbols in figure 6-22.The addition symbol (+) identifies the ORoperation. The multiplication symbol or dot (•)identifies the AND operation, and you may also useparentheses and other multiplication signs.Logic OperationsFigure 6-23 shows the three basic logic operations(AND, OR, and NOT) and four of the simplercombinations of the three (NOR, NAND, INHIBIT,and EXCLUSIVE OR). For each operation, the figurealso shows a representative switching circuit, a truthtable, and a block diagram. In some instances, it showsmore than one variation to illustrate some specificpoint in the discussion of a particular operation. In allcases, a 1 at the input means the presence of a signalcorresponding to switch closed, and a 0 represents theabsence of a signal, or switch open. In all outputs, a 1represents a signal across the load, a 0 means no signal.For the AND operation, every input line must havea signal present to produce an output. For the ORoperation, an output is produced whenever a signal ispresent at any input. To produce a no-outputcondition, every input must be in a no-signal state.In the NOT operation, an input signal produces nooutput, while a no-signal input state produces anoutput signal. (Note the block diagrams representingthe NOT circuit in the figure.) The triangle is thesymbol for an amplifier, and the small circle is thesymbol for the NOT function. The circle is used toindicate the low-level side of the inversion circuit.OperationMeaningA•BA AND BA + BA OR BAA NOT or NOT A(A + B) (C)A OR B, AND CAB+CA AND B, OR CA•BA NOT, AND BFigure 6-22.—Logic symbols.6-22

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