In this article, we will study the concepts of the NAND gate, a universal logic gate in digital electronics. So, let us begin with the definition of the NAND gate.
Definition of NAND Gate
The NAND Gate, also called NOTed AND Gate is a universal
logic gate used in digital electronic systems to perform logical inversion of
AND operation.
The NAND gate produces a LOW (logic 0) output only when all
its inputs are HIGH (Logic 1). For all other combinations of inputs, the NAND
gate produces a HIGH (Logic 1) output.
Therefore, the NAND gate is also known as the inverse of the AND
gate. Similar to any other logic gate, a NAND gate can also have two or more
input lines and one output line.
Also, the NAND gate is a universal logic gate, as it can be
used to implement any other type of logic gate or Boolean function without the need
for any other type of logic gate.
NAND Gate using Basic Logic Gates
As the NAND gate is a combination of AND gate and NOT gate.
Therefore, it can be realized by using an AND gate and a NOT gate as shown in
the following figure.
Logic Symbol of NAND Gate
The following figure shows the logic symbol of a two-input
NAND gate.
The following figure shows the logic symbol of a three-input NAND gate.
Truth Table of NAND Gate
The truth table of a two-input NAND gate is given below:
|
Inputs |
Output |
|
|
A |
B |
Y |
|
0 |
0 |
1 |
|
0 |
1 |
1 |
|
1 |
0 |
1 |
|
1 |
1 |
0 |
The following is the truth table of a three-input NAND gate:
|
Inputs |
Output |
||
|
A |
B |
C |
Y |
|
0 |
0 |
0 |
1 |
|
0 |
0 |
1 |
1 |
|
0 |
1 |
0 |
1 |
|
0 |
1 |
1 |
1 |
|
1 |
0 |
0 |
1 |
|
1 |
0 |
1 |
1 |
|
1 |
1 |
0 |
1 |
|
1 |
1 |
1 |
0 |
Boolean Function of NAND Gate
We can obtain the logical expression or Boolean function of
a two-input NAND gate directly from its truth table. The following is the Boolean
expression of a two-input NAND gate.
Where A and B are inputs and Y is the output. The above
expression is read as Y is equal to A AND B bar.
Similarly, we can also derive the Boolean function of a three-input NAND gate from its truth table. The following is the Boolean expression of a three-input NAND gate.
`\Y=(A.B.C)'=\overline{A.B.C}`
In this case, there are three inputs namely, A, B, and C, and only one output, i.e. Y.
Switching Circuit Diagram of NAND Gate
The following figure depicts the
switching circuit diagram of a two-input NAND gate.
It consists of two switches A and B, a battery, and a lamp.
When both switches A and B are
closed, i.e. both inputs are high, no current will flow through the lamp,
turning the lamp off.
When any of the switches are open, the
total current will follow the path through the lamp, turning the lamp on.
This way, the above-shown switching circuit
implements the NAND operation.
NAND Gate Transistor Circuit
The construction of a two-input NAND gate
using two BJT transistors is shown in the following figure.
This construction of the NAND gate is also known as RTL NAND gate or Resistor-Transistor Logic NAND gate.
In this circuit, when both inputs A and B
are HIGH (+5 V), the transistors T1 and T2 are on,
providing a path for current to flow from the supply (+VCC) to the ground.
Hence, the total voltage will go to the ground, making the output low.
When any of the inputs are LOW (0 V),
making the corresponding transistor off. Hence, there will be no path for the
flow of current from the supply (+VCC) to the ground. Therefore, the total
supply voltage will be available at the output, making it high.
7400 NAND Gate IC
The construction of the 7400 NAND gate IC
is shown in the following figure. The 7400 IC is a quad 2-input logic NAND gate
IC used in various electronics systems.
Applications of NAND Gate
The following are some key applications
of NAND gate:
- NAND gate is used in alarm circuits.
- NAND gate is also used in burglar alarms.
- NAND gate is also used in automatically operated doors and windows.
- NAND gates are also used in the freezer warning buzzer system.
- NAND gate is also used in automatic temperature control systems.
Hence, this is all about the NAND gate, its
truth table, logic symbol, Boolean formula, and applications.
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