Digital Logic or Boolean Logic
Basically the Digital Logic or Boolean Logic represents the signals and sequences in a digital circuit through binary numbers. It is a system of rules that allow us to make complicated decisions based on simple LOW / High, NO / YES questions. Its makes the foundation of digital computing and explains how hardware and circuits communicate within a computer. Actually the Digital logic is the basis on computing and many other electronic devices as well as control systems found in this continually advancing digital world. It constructs to implementation of computer operations by manipulating the binary values through printed circuit board technology that uses circuits and basic logic gates. Most electronic devices, including computers, calculators, watches, and video games and contain this feature. Awareness or Knowledge in digital logic can be an advantage for many people who worked with computers and Digital electronics technology like engineers and technicians.
Basic Logic NOT Gate or Invertor
The Logic NOT Gate or invertor is the most basic of all the
basic logic gates and is often referred to as an Inverting Buffer or simply an
Inverter.
Inverting “NOT” Gate is single input device which having just
one input “Q" and one output the complement of "Q" that is
normally at logic level HIGH and goes “LOW” to a logic level LOW when its
single input is at logic level HIGH, in other words we can say that it
“inverts” (complements) its input signal. The output from a NOT Gate only
returns “HIGH” again when its input “A” is at logic level LOW or “0” giving us
the Boolean expression of: Q = 
thus we can define the operation of NOT Gate or invertor like a
single input digital logic NOT gate as being:
“If
A is NOT true, then Q is true”
Transistor Logic
NOT Gate
A simple single input logic NOT Gate can be constructed using a
RTL Resistor-transistor switch as shown below with the input connected directly
to the transistor base. thus the transistor must be saturated “ON” for an
inverted. output “OFF” at Q.
Logic NOT Gates are
available to use in digital logic circuits to produce the desired logical
operational functions. The standard invertor or "NOT" Gate is given a
symbol whose shape is of a triangle pointing to the right with a circle at its
end. The circle is known as a mark like
“inversion bubble” and its used in NOT, NAND and NOR symbols at their output to
represent the logical operation of the NOT function. The bubble denotes the
signal inversion (complementation) of the signal like "0" to
"1" and "1" to "0" can be present on either or
both the output and/or the input terminals.
AND Gate
We
can easily understand the AND Gate logic by using the transistors because we
know that how to transistor work thus we can easily construction the logic
gates that are depends upon their utility as fastest switches. When the base
and emitter junction is turned on enough to be driven into saturation, the
collector voltage with respect to the emitter may be near zero and mat be used
to construct the logic gates for the TTL logic family.
Logic
AND Function
The Basic Logic Gate AND Function output will only just true when all of the inputs of them are true, otherwise the output will false.
Boolean Algebra is based
around basic logical functions in which each of the Boolean function, such as
the basic logic AND function, typically has one or more inputs value and
produces an output result based on these inputs value. The inputs have one of
two values: True (1) or False (0).
during the 1854, George
Boole performed an investigation into the “laws of thought” which were based
around a simplified version of the “group” or “set” theory, and from this
Boolean Algebra was developed. Boolean Algebra deals mainly with the theory
that both logics and sets operations are either (1) “TRUE” or (0) “FALSE” but
not both at a time.
For example, A + A = A and
not 2A as it would be in normal algebra. Boolean Algebra is an effective and
simple ways of representing the switching action in all the standard Logic
Gates and the basic logic statements which concern us here are given by the
basic logic gate operations of the AND, the OR and the invertor or NOT gate
functions.
The logic AND
Function
The Basic Logic Gate AND
Function states that two or more events must occur all together and at the same
time for an output action to occur. This sequence in which these actions occur
is unimportant as it does not affect the final result. For example, A & B =
B & A. In Boolean algebra the Basic Logic gate AND Function follows the
"Commutative Law" which allows the change in position of either
variable.
The Basic logic AND function is
represented in digital electronics by the full stop or "dot" symbol
like this ( . ) Thus a 2 - input (A B) Basic logic AND Gate has an output term
represented by the Boolean Expression like this A.B or just AB.
Switch
Representation of the AND Function
There are the two
switches, A and B are connected together in the form of a series circuit.
Therefore, in the circuit above, both switches “A” and “B" must be closed
(Logic “1” or “High”) in sequence to put the lamp on. In other words, we can
say that the both of switches must be closed, or at (logic “1” or “High")
for the lamp to be “ON” condition.
Then this type of basic
logic gate (an AND Gate) only produces an output when “ALL” of its inputs are
present. In Boolean Algebra terms the output will be "High" or
"1" only when all of its inputs are "High". In terms
electrical, the logic AND function is equal to a series circuit as shown above figure.
As
there are only two A and B Switches, each with two possible states “open” or
“closed”. Defining a Logic “0” or LOW as being when the switch is open and a
Logic “1” High when the switch is closed, there are then four different ways or
combinations of arranging the two switches together as shown.
There
is a table to display the using terminologies as input or out puts in digital
electronics to operate the Basic Logic Gate or other local circuit and
systems.
Truth Table for AND Gate
OR GATE
OR Gate
As well as the OR gate gives high at the output when either of the inputs is high or both the inputs are high, otherwise it gives low. The uses of transistors for represent the "OR" gate operation depends on the transistor's switching mode, speed. For the Basic Logic "OR" gate operation, we used the two transistors as the switches.
Logic OR Function
The Basic
Logic Gate "OR" function output is only true if one or more of
its inputs are true, otherwise the output is false.
The Basic
Logic Gate "OR" Function states that an output action will become
"TRUE" if either one “OR” more events are TRUE, but the order at
which they occur is unimportant as it doesn’t affect the final result.
For example, A + B = B + A. In Boolean algebra
the Logic OR Function follows the “Commutative
Law” the same as for the logic AND function, allowing a change in position
of either variable.
The Basic Logic Gate "OR" function is mostly called by
its full name of “Inclusive OR” in contrast to the Exclusive - OR function we
will look at later another blog.
The logic or Boolean expression given for a Basic logic "OR" gate is that for Logical Addition which is denoted by a plus sign, (+). Thus a 2 - input (A B) Logic "OR" Gate has an output term represented by the Boolean expression of: A+B = Z.
Switch
Representation of the OR Function
There are the two switches A and
B are connected in parallel and either Switch B OR Switch A can be closed in
sequence or order to put the lamp on. In other words, we can say that either
switch can be closed, or at logic "High" / “1” for the lamp to be
“ON”.
Then this type of Basic logic
gate only produces and output when “ANY” of its inputs are present and in
Boolean Algebraic terms the output will be "High" / TRUE when any of
its inputs are "High"/ TRUE. In electrical terms, the Basic logic OR
function is equal to a parallel circuit.
Again as with the Basic Logic AND function there are two switches, each with two possible positions open or closed so therefore there will be 4 different ways of arranging the switches.
Logic OR Function Truth Table
Logic OR gates are available as standard (integrated circuit)
I-C packages such as the common TTL
74LS32 Quadruple 2-input Positive OR Gates. As with the previous AND Gate, OR can also be “cascaded” together to produce circuits with more inputs such as in security alarm systems (Zone A or Zone B or Zone C, etc.).
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