
Digital Logic Design
Derived Gates
While the three basic functions AND, OR, and NOT are sufficient to
accomplish all possible logical functions and operations, some combinations
are used so commonly that they have been given names and logic symbols of
their own.
We will discuss three of these on this page. The first is called NAND,
and consists of an AND function followed by a NOT function. The second, as
you might expect, is called NOR. This is an OR function followed by NOT. The
third is a variation of the OR function, called the ExclusiveOR, or XOR
function. As with the three basic logic functions, each of these derived
functions has a specific logic symbol and behavior, which we can summarize
as follows:
The NAND Gate
The NAND gate implements the NAND function, which is exactly inverted
from the AND function you already examined. With the gate shown to the left,
both inputs must have logic 1 signals applied to them in order for the
output to be a logic 0. With either input at logic 0, the output will be
held to logic 1.
The
circle at the output of the NAND gate denotes the logical inversion, just as
it did at the output of the inverter. Also in the figure to the left, note
that the overbar is a solid bar over both input values at once. This shows
that it is the AND function itself that is inverted, rather than each
separate input.
As with AND, there is no limit to the number of inputs that may be
applied to a NAND function, so there is no functional limit to the number of
inputs a NAND gate may have. However, for practical reasons, commercial NAND
gates are most commonly manufactured with 2, 3, or 4 inputs, to fit in a
14pin or 16pin package.
The NOR Gate
The NOR gate is an OR gate with the output inverted. Where the OR gate
allows the output to be true (logic 1) if any one or more of its inputs are
true, the NOR gate inverts this and forces the output to logic 0 when any
input is true.
In symbols, the NOR function is designated with a
plus sign (+), with an overbar over the entire expression to indicate the
inversion. In logical diagrams, the symbol to the left designates the NOR
gate. As expected, this is an OR gate with a circle to designate the
inversion.
The NOR function can have any number of inputs, but practical commercial
NOR gates are mostly limited to 2, 3, and 4 inputs, as with other gates in
this class, to fit in standard IC packages.

The ExclusiveOR, or XOR Gate

The
ExclusiveOR, or XOR function is an interesting and useful variation on
the basic OR function. Verbally, it can be stated as, "Either A or B, but
not both." The XOR gate produces a logic 1 output only if its two inputs
are different. If the inputs are the same, the output is a logic 0.
The XOR symbol is a variation on the standard OR symbol. It consists of
a plus (+) sign with a circle around it. The logic symbol, as shown here,
is a variation on the standard OR symbol.
Unlike standard OR/NOR and AND/NAND functions, the XOR function always
has exactly two inputs, and commercially manufactured XOR gates are the
same. Four XOR gates fit in a standard 14pin IC package.
The three derived functions shown above are by no means the only ones,
but these form the basis of all the others.
Source:
http://www.playhookey.com
Digital Logic Design Home  Academics Home 