Unformatted text preview: A4 Appendix A w the NOR function to be true, all of the variables
must be false. The function is false when one or
more of the variables is true. The logic circuit for the NOR function is an OR
gate followed by an inverter as shown in Fig. A5
(a). These two circuits are usually combined into a
single NOR gate as shown in the symbol of (b).
As with previous NOT functions, the small circle
at the output of the NOR gate indicates inversion.
The fundamental true and false relationships of the
NOR gate are shown in the truth table of (c). The
general forms of the NOR equation are: A+B+C+....=X MgAs The EXCLUSIVE OR Function. The EXCLUSIVE
OR (XOR) operation is a special case of the OR
operation. An XOR logic statement yields a true
result only when an odd number of variables are
true. Conversely, a false results when an even
number of variables are true. For an XOR statement
having two variables, this means that a true result
is obtained when one or the other of the variables
is true, but not when both are true. This latter
condition is what distinguishes the XOR operation
from the regular OR operation, that is, it excludes
the condition whereby both variables are true.
Thus, for the twovariable XOR statement, there
are two conditions by which a false result is
obtained and that is when both variables are true
or both are false. The XOR operation having two variables can be
implemented using the logic circuit shown in
Fig. A6 (a). Other configurations are possible
depending on the logic components available,
but the logic symbol of (b) is commonly used to
indicate the XOR operation regardless of the type
of circuit. It can be seen from the logic circuit why
the XOR function excludes the all 0's or all 1’s
states. For example, if variables A and B are both
true, the inverters insure that one input to each
AND gate is 0, resulting in a 0 output from both AND gates and thus the output OR gate. If both
input variables are false, the inverters insure that
one input to each AND gate is 1, again resulting
in a 0 output from both AND gates and the
output OR gate. It is only when one variable is
true while the other one is false that either AND
gate has 1 ’s on both inputs and produces a 1 output
from the XOR circuit. The truth table of (c) lists
all possible combinations of the XOR gate input
output conditions just described. The expanded form of the two variable XOR
equation is generally stated as: X=A§+EB This expression is sometimes referred to as an
inequality statement and its circuit referred to as
an inequality comparator. The XOR function is
commonly signified in condensed form in terms of
the input variable only, separated by a connective
made up of the OR symbol enclosed in a circle
(69). The condensed two variable XOR equation
thus becomes: X=A63B xaBJn
A'.—B IGJ [M M Fig. A6 The EXCLUSIVE NOR Function. The EXCLU
SIVE NOR (XNOR) operation is the complement
of the XOR operation, or it can be viewed as a
special case of the NOR operation. The XNOR
operation is indicated by a NOT symbol placed
over an XOR logic expression. An XNOR logic
statement yields a true result only when an even
number of variables are identical. Conversely, a false
results for any other combination of variables. For
an XNOR statement having two variables, this
means that a true result is obtained when both
variables are true or both are false, and that a false
result is obtained when only one variable is true.
This is the exact opposite or complement of the ...
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 Fall '05
 Myer,B

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