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logic gate & simple logic circuit
Introduction
Boolen Algebra name from George Boole (mathematician) can convert human ways of expressing logical processes into a mathematical and electronic form for computation known as symbolic iogic, or Boolen Algebra.
computers are built as collection of switches that either "on" or "off", Boolen Algebra is a very natural way to present digital information.
Boolen Algebra is a logical algebra.
the variables take on two values corresponding to truth (1 or T) and false (0 or F).
logic gate & simple logic circuit
Introduction
Boolen Algebra name from George Boole (mathematician) can convert human ways of expressing logical processes into a mathematical and electronic form for computation known as symbolic iogic, or Boolen Algebra.
computers are built as collection of switches that either "on" or "off", Boolen Algebra is a very natural way to present digital information.
Boolen Algebra is a logical algebra.
the variables take on two values corresponding to truth (1 or T) and false (0 or F).
value 1 represent true (T)
value 0 represent false (F)
Boolen Algebra use three basic logical operators : AND , OR and NOT.
A logic gate is an elementary building
block of a digital circuit. Most logic gates have two inputs and
one output. At any given moment, every terminal is in one of the two binaryconditions low (0)
or high (1), represented by different voltage levels.
The logic state of a terminal can, and generally does, change often, as the
circuit processes data. In most logic gates, the low state is approximately
zero volts (0 V), while the high state is
approximately five volts positive (+5 V).
There are seven basic logic gates: AND,
OR, XOR, NOT, NAND, NOR, and XNOR.
The AND gate is so
named because, if 0 is called "false" and 1 is called
"true," the gate acts in the same way as the logical "and"
operator. The following illustration and table show the circuit symbol and
logic combinations for an AND gate. (In the symbol, the input terminals are at
left and the output terminal is at right.) The output is "true" when
both inputs are "true." Otherwise, the output is "false."
AND gate
Input 1
|
Input 2
|
Output
|
|
|
|
|
1
|
|
1
|
|
|
1
|
1
|
1
|
The OR gate gets its
name from the fact that it behaves after the fashion of the logical inclusive
"or." The output is "true" if either or both of the inputs
are "true." If both inputs are "false," then the output is "false."
OR gate
Input 1
|
Input 2
|
Output
|
|
|
|
|
1
|
1
|
1
|
|
1
|
1
|
1
|
1
|
A logical inverter ,
sometimes called a NOT gate to differentiate it from other
types of electronic inverter devices, has only one input. It reverses the logic
state.
Inverter or NOT gate
Input
|
Output
|
1
|
|
|
1
|
The NAND gate operates
as an AND gate followed by a NOT gate. It acts in the manner of the logical
operation "and" followed by negation. The output is "false"
if both inputs are "true." Otherwise, the output is "true."
NAND
gate
Input 1
|
Input 2
|
Output
|
|
|
1
|
|
1
|
1
|
1
|
|
1
|
1
|
1
|
|
The NOR gate is a
combination OR gate followed by an inverter. Its output is "true" if
both inputs are "false." Otherwise, the output is "false."
NOR
gate
Input 1
|
Input 2
|
Output
|
|
|
1
|
|
1
|
|
1
|
|
|
1
|
1
|
|
Using combinations of logic gates,
complex operations can be performed. In theory, there is no limit to the number
of gates that can be arrayed together in a single device. But in practice,
there is a limit to the number of gates that can be packed into a given
physical space. Arrays of logic gates are found in digital integrated circuits
(ICs).
As IC technology advances, the required physical volume for each individual
logic gate decreases and digital devices of the same or smaller size become
capable of performing ever-more-complicated operations at ever-increasing
speeds.
for example
i finally understand this topic. tq!
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