In digital electronics, there are several different types of logic gates such as AND gate, OR gate, NOT gate, etc. In this chapter, we will explain the theory of AND gate.

An AND gate is a basic logic gate used to implement various complex digital circuits and systems. The AND gate performs the logical multiplication of inputs applied to it and produces an output accordingly.

What is an AND Gate?

An AND gate is a type of basic logic gate used in various digital circuits and systems. It produces a high or logic 1 or True output, only when all its inputs are high or logic 1 or true. For all other combinations of inputs, it produces a low or logic 0 or False output.

The logic symbols for the two and three input AND gates are depicted in the following figure.

Here, A, B, and C are the input variables and Y is the output variable.

In this chapter, we will cover AND gates having three inputs only. But we can design an AND gate for any number of input variables.

Truth Table of AND Gate

The truth table of an AND gate contains inputs and outputs, and specifies the relationship between them.

The truth table of a two-input AND gate is given below −

From this truth table of two-input AND gate, it can be observed that the output of the AND gate is logic 1 or high, only when both inputs are logic 1 or high.

The following table represents the truth table of a three-input AND gate −

This truth table shows that the output is high or logic 1 only when all the three inputs to the AND gate are high or logic 1. For rest input combinations, the output is low or logic 0.

From these truth tables of AND gate, we can conclude that an AND gate produces a high or logic 1 output, only when all its inputs are high or logic 1, otherwise the output is low or logic 0.

Working of AND Gate

The working of a two-input AND gate is explained below −

• If A = 0 and B = 0, the output is low i.e., Y = 0.
• If A = 0 and B = 1, the output is low i.e., Y = 0.
• If A = 1 and B = 0, the output is low i.e., Y = 0.
• If A = 1 and B = 1, the output is high i.e., Y = 1.

The working of a three-input AND gate is explained below −

• If A = 0, B = 0, and C = 0, the output is low i.e., Y = 0.
• If A = 0, B = 0, and C = 1, the output is low i.e., Y = 0.
• If A = 0, B = 1, and C = 0, the output is low i.e., Y = 0.
• If A = 0, B = 1, and C = 1, the output is low i.e., Y = 0.
• If A = 1, B = 0, and C = 0, the output is low i.e., Y = 0.
• If A = 1, B = 0, and C = 1, the output is low i.e., Y = 0.
• If A = 1, B = 1, and C = 0, the output is low i.e., Y = 0.
• If A = 1, B = 1, and C = 1, the output is high i.e., Y = 1.

This is all about working of a two-input and a three-input AND gates.

Boolean Expression of AND Gate

Boolean expression is a logic equation or a logic function that represents the mathematical relationship between inputs and output of the AND gate.

The Boolean expression of a two-input AND gate is given by,

Y = A · B

Where, A and B are inputs and Y is the output. This expression is read as “Y is equal to A AND B.” The dot (·) symbol represents the AND operation.

For the three-input AND gate, the Boolean expression is given by,

Y = A · B · C

It is read as “Y is equal to A AND B AND C”.

In the same way, we can obtain the Boolean expression for an AND gate having any number of input variables.

AND Gate using Transistor

The transistor circuit of a two-input AND gate is shown in the following figure.

The implementation of AND gate using transistors requires as many transistors as the number of inputs. For example, a two-input AND gate requires two transistors.

Working of Transistor AND Gate

The working the transistor AND gate shown in the above figure is explained below −

When both inputs A and B are low, the transistors Q₁ and Q₂ remain in off state and act as open switch. Therefore, the output line Y will directly connect to the ground potential. Thus, the output is low or logic 0.

When the input A is low and the input B is high, the first transistor Q₁ is off and the second transistor Q₂ is on. But still the supply voltage will not connect to the output line and the output line will remain at ground potential. Consequently, the output is low or logic 0.

When the input A is high and the input B is low, the transistor Q₁ will conduct and the transistor Q₂ will remain off. In this condition, the output line does not receive the supply voltage but connect to the ground potential. Hence, for this input combination, the output is low or logic 0.

When both inputs A and B are high, both transistors Q₁ and Q₂ will turn on and act as closed switches. In this condition, the supply voltage directly connect to the output line. This makes output of the circuit high or logic 1.

This is how the above transistor circuit acts a two-input AND gate. We can add more transistors to implement a high order AND gate.

AND Gate using Switches

We can also implement AND gate logic using a battery, switches, and a lamp or bulb. The following figure shows the AND gate using switches.

In this AND gate circuit, we have a voltage source, two switches representing two input terminals of the AND gate, and a lamp representing the output.

From the circuit, we see that if both switches A and B are closed, there will be a closed for current to flow in the circuit. Hence, the lamp will glow that represents the high or logic 1 output.

If both or any of the two switches be open, there will be a break in the current path, making the lamp off. This represents the low or logic 0 state of the output of the AND gate.

This way, the above depicted switching circuit performs the AND gate operation. By adding more number of switches in series, we can implement a higher order AND gate.

AND Gate IC

In practice, there is an integrated circuit namely, IC 7408 which is a most commonly used AND gate IC. This AND gate IC is implemented in transistor-transistor logic (TTL). The block diagram of the AND gate IC 7408 is shown in the following figure.

It is a Quad-2 AND gate IC having four two-input AND gates integrated on a single chip. It has 14 pins.

Conclusion

In conclusion, the AND gate is a fundamental logic gate used in digital circuits to implement the Boolean multiplication function.

The output of the AND gate is high or logic 1 only when all its inputs are high or logic 1. Otherwise, it generates a low or logic 0 output.

AND gate plays an important role in various digital electronic applications such as data processing, memory devices, arithmetic logic units, control systems, and more.