Many
designers need knowledge of basic digital circuits and logic. We were
getting many feedbacks from readers who know the programming and want to
have some idea of digital basics for interfacing or related works. We are
working to bring some more articles on Boolean algebra and bitwise
operations in programming. This is the first article in this series.
Logic gates forms
the basic structural and functional part of the digital electronic
circuits. Basically a logic gate is a circuit which
Ř
Combines two or more signals to give different signal of any logical or
mathematical operation of the given signals.
Ř
Gives
the complement or negative of the given signals.
Different
types of logic gates available are
Inverter/NOT gate
AND gate
OR gate
NAND gate
NOR gate
XOR gate
XNOR gate
Normally a
signal is called either HIGH or LOW in digital electronics. There are two
logic conventions to give values of HIGH and LOW.
Positive logic: HIGH 1
(+5V)
LOW
0
(0V)
Negative logic:
HIGH 0
(0V)
LOW
1
(+5V)
Hereafter
we use positive logic in our discussion.
Inverter/NOT gate:
Symbol:
Operation:
When a
HIGH signal is given as input to an inverter, a LOW pulse will appear as
output or viceversa. The operation is summarized in truth table.
Truth table:
When to use:
Whenever a
signal or pulse has to be inverted we use inverter/NOT gate.
Note:
The bubble
indicated at the output of NOT gate is called negation indicator. When
appearing on output, the bubble means that an internal ‘1’ produces an
external ‘0’.
AND gate:
Symbol:
Operation:
The AND
gate performs logical multiplication more commonly known as AND function.
It may have more than two inputs and only one output.
When all
the inputs are HIGH, the output is HIGH.
When at
least one of the inputs is LOW, the output is LOW.
Truth table:
inputs 
output 
A 
B 
C 
0 
0 
0 
0 
1 
0 
1 
0 
0 
1 
1 
1 
When
to use:
To
determine when certain conditions are simultaneously true, as indicated by
HIGH levels.
Note:
We
generally express the logical operation of a gate with a table that lists
all input combinations and corresponding outputs. This table of
combinations is called a truth table. When we have two inputs there are 4
combinations of inputs. Similarly if we have ‘n’ inputs we get ‘2^{n’
}combinations.
OR
gate:
Symbol:
Operation:
The OR
gate performs logical addition more commonly called OR function. It may
have more than two inputs but only one output.
When at
least one of the inputs is HIGH, output is HIGH.
When all the inputs are LOW, output is LOW.
Truth table:
inputs 
output 
A 
B 
C 
0 
0 
0 
0 
1 
1 
1 
0 
1 
1 
1 
1 
When
to use:
To check whether at
least one of the inputs is HIGH.
NAND gate:
Symbol:
Operation:
The term
NAND is a contraction of NOTAND and implies an AND function with a
complemented output.
When all
the inputs are HIGH, the output is LOW.
When at least one of the inputs is LOW, the output is HIGH.
Truth table:
inputs 
output 
A 
B 
C 
0 
0 
1 
0 
1 
1 
1 
0 
1 
1 
1 
0 
Corollary:
The NAND
is a very logic function because it is a “Universal Function” i.e. it can
be used to construct an AND gate or an OR gate, an inverter or any
combination of these functions.
Construction
of AND, OR, NOT gates using NAND gate:
NOT gate:
Here both the
inputs are same i.e. a, hence by the function of NAND we get a’ as output.
This is also output of NOT gate.
AND gate:
The
output of NAND gate is given as two inputs to another NAND gate to get AB,
the output of an AND gate.
OR gate:
The OR can
be implemented by use of NAND gates using basic Boolean Algebra.
When to use:
When there
are different types of gates are required, all of them can be replaced by
NAND gates only.
NOR:
Symbol:
Operation:
The
term NOR is a contraction of NOTOR and implies an OR function with an
inverted output.
When all the inputs are LOW, output is HIGH.
When at least one of the inputs is HIGH, output is LOW.
Truth
table:
inputs 
output 
A 
B 
C 
0 
0 
1 
0 
1 
0 
1 
0 
0 
1 
1 
0 
Corollary:
Nor gate
is also a universal gate because NOR function can be used to construct
AND, OR, NOT or any combination of these functions.
NOT:
OR:
AND:
When to use:
When there
are different types of logic gates are required, they can be replaced by
NOR gates.
XOR gate:
Symbol:
Operation:
The
acronym for XOR is ExclusiveOr. It is a widely used function because of
special arithmetic properties. A special exclusiveor symbol, is
used.
When all
the inputs are identical, HIGH/LOW, the output is LOW.
When the inputs have different logic levels, the output is HIGH.
Truth table:
inputs 
output 
A 
B 
C 
0 
0 
0 
0 
1 
1 
1 
0 
1 
1 
1 
0 
Use:
It is used
in adder circuits, comparator circuits.
XNOR gate:
Symbol:
Operation:
XNOR is a
contraction of ExclusiveNOTOR and implies a XOR function with an
inverted output.
When all the inputs are identical, HIGH/LOW, the output is HIGH.
When all inputs have different logic levels, the output is LOW.
Truth table:
inputs 
output 
A 
B 
C 
0 
0 
1 
0 
1 
0 
1 
0 
0 
1 
1 
1 
