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 relationships 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.

Figure 6-22.-Logic symbols.

Figure 6-23.-Logic operations comparison chart.

The NOR operation is simply a combination of an OR operation and a NOT operation. In the truth table, the OR operation output is indicated between the input and output columns. The switching circuit and the block diagram also indicate the OR operation.

The NAND operation is a combined operation, comprising an AND and a NOT operation.

The INHIBIT operation is also a combination AND and NOT operation, but the NOT operation is placed in one of the input legs. In the example shown, the inversion occurs in the B input leg; but in actual use, it could occur in any leg of the AND gate.

The EXCLUSIVE OR operation differs from the OR operation in the case where a signal is present at every input terminal. In the OR, an output is produced; in the EXCLUSIVE OR, no output is produced. In the switching circuit shown, both switches cannot be closed at the same time; but in actual computer circuitry, this may not be the case. The accompanying truth tables and block diagrams show two possible circuit configurations. In each case the same final results are obtained, but by different methods.

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