Logic diagrams are used in the operation and
maintenance of digital computers. Graphic symbols
from ANSI Y32.14 are used in these diagrams.
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
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 operationsaddition, subtraction,
multiplication, and division. Boolean algebra uses
three basic operationsAND, 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.
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.
A AND B
A + B
A OR B
A NOT or NOT A
(A + B) (C)
A OR B, AND C
A AND B, OR C
A NOT, AND B
Figure 6-22.Logic symbols.