LOGIC DIAGRAMS Logic diagrams are used in the operation and maintenance  of  digital  computers.  Graphic  symbols from  ANSI  Y32.14  are  used  in  these  diagrams. Computer Logic Digital   computers   are   used   to   make   logic decisions about matters that can be decided logically. Some examples are when to perform an operation, what  operation  to  perform,  and  which  of  several methods to follow. Digital computers never apply reason and think out an answer. They operate entirely on instructions prepared by someone who has done the thinking  and  reduced  the  problem  to  a  point  where logical decisions can deliver the correct answer. The rules for the equations and manipulations used by a computer often differ from the familiar rules and procedures  of  everyday  mathematics. People  use  many  logical  truths  in  everyday  life without  realizing  it.  Most  of  the  simple  logical patterns are distinguished by words such as and, or, not, if, else,  and  then.  Once the verbal reasoning process  has  been  completed  and  results  put  into statements, the basic laws of logic can be used to evaluate   the   process.   Although   simple   logic operations can be performed by manipulating verbal statements,  the  structure  of  more  complex  relation- ships can more usefully be represented by symbols. Thus, the operations are expressed in what is known as symbolic logic. The symbolic logic operations used in digital computers are based on the investigations of George Boole, and the resulting algebraic system is called Boolean algebra. The objective of using Boolean algebra in digital computer study is to determine the truth value of the combination  of  two  or  more  statements.  Since Boolean algebra is based upon elements having two possible stable states, it is quite useful in representing switching circuits. A switching circuit can be in only one of two possible stable states at any given time; open or closed. These two states may be represented as 0 and 1 respectively. As the binary number system consists of only the symbols 0 and 1, we can see these symbols with Boolean algebra. In the mathematics with which you are familiar, there are four basic operations—addition, subtraction, multiplication, and division. Boolean algebra uses three basic operations—AND, OR, and NOT. If these words do not sound mathematical, it is only because logic began with words, and not until much later was it  translated  into  mathematical  terms.  The  basic operations are represented in logical equations by the symbols in figure 6-22. The  addition  symbol  (+)  identifies  the  OR operation.  The  multiplication  symbol  or  dot  (•) identifies the AND operation, and you may also use parentheses and other multiplication signs. Logic Operations Figure 6-23 shows the three basic logic operations (AND,  OR,  and  NOT)  and  four  of  the  simpler combinations of the three (NOR, NAND, INHIBIT, and EXCLUSIVE OR). For each operation, the figure also shows a representative switching circuit, a truth table, and a block diagram. In some instances, it shows more than one variation to illustrate some specific point in the discussion of a particular operation. In all cases, a 1 at the input means the presence of a signal corresponding to switch closed, and a 0 represents the absence of a signal, or switch open. In all outputs, a 1 represents a signal across the load, a 0 means no signal. For the AND operation, every input line must have a signal present to produce an output. For the OR operation, an output is produced whenever a signal is present   at   any   input.   To   produce   a   no-output condition, every input must be in a no-signal state. In the NOT operation, an input signal produces no output, while a no-signal input state produces an output  signal.  (Note  the  block  diagrams  representing the NOT circuit in the figure.) The triangle is the symbol for an amplifier, and the small circle is the symbol for the NOT function. The circle is used to indicate the low-level side of the inversion circuit. Operation Meaning A•B A AND B A + B A OR B A A NOT or NOT A (A + B) (C) A OR B, AND C AB+C A AND B, OR C A•B A NOT, AND B Figure 6-22.—Logic symbols. 6-22