# AND Gate – Symbol, Truth table & Realization

AND gate is a device which has two or more inputs and one output. The output of an AND gate is logical 1 only if all the inputs are logical 1. In Boolean algebra, the term AND is represented by dot (.) and the Boolean expression Y = A.B indicates Y equals A AND B.

Contents

## AND gate Symbol

The AND gate logic symbol is shown in figure 1.

## Truth table of AND gate

The truth table of AND gate is given below.

 A B Y = A.B 0 0 0 0 1 0 1 0 0 1 1 1

## AND gate Circuit Diagram

The AND gate can be realised by the electronic circuit by using two ideal p-n junction diodes D1 and D2 as shown in fig. 2.

The resistance R is connected to the positive terminal of a 5 V battery. The output voltage is Y w.r.t. ground. The operation of AND gate can be understood by the following four cases.

Case-1: When both A and B are connected to earth (i.e. A = 0 and B = 0)

In this case, both the diodes D1 and D2 get forward biased and hence conduct. The diodes being ideal, no voltage drop takes place across either diode. Therefore, a voltage drop of 5 V takes place across R, with Y at zero potential w.r.t. earth. Thus the output Y is at logical 0.

Case-2: When A is earthed and B is connected to positive terminal of battery of 5 V (i.e. A = 0 and B = 1)

In this case, the diode D1 will conduct while D2 will not conduct. Since diode D1 is ideal, no voltage drop takes place across D1. Therefore, a voltage drop of 5 V takes place across R, having Y at zero volt w.r.t. earth. Now the output Y is at logical 0.

Case-3: When A is connected to positive terminal of battery of 5 V and B is earthed (i.e. A = 1 and B = 0)

In this case, the diode D2 will conduct while D1 will not conduct. Since D2 is ideal, no voltage drop takes place across D2. Therefore, a voltage drop of 5 V takes place across R, having Y at zero volt w.r.t. earth. Now the output Y is at logical 0.

Case-4: When A and B both are connected to positive terminal of battery of 5 V (i.e. A = 1 and B = 1)

In this case, none of the diodes will conduct. There will be no current through resistance R. Now potential at Y is equal to potential +5 V w.r.t. earth. Hence the output Y is at logical 1.

Hence it can be concluded that the output of AND gate is at logical 1 only if all the inputs are at logical 1.

## Switch Circuit of AND gate

The switch circuit having function similar to the AND gate is shown in figure 3.

In this arrangement switch OFF (or open) corresponds to logical 0 and switch ON (or closed) corresponds to logical 1. The inputs are introduced through the switches A and B. The lighting of the bulb Q is the output. Here we find that the bulb glows (i.e. output is 1) only when both the switches A and B are closed. The bulb remains off (i.e. output is 0) when either switch A or switch B or both are open.

## AND gate using NAND gate

To produce AND gate using NAND gate, the output of the NAND gate is connected to the NOT gate (made from NAND gate by joining the two inputs) as shown in fig. 4.

The truth table of the above combination is given below.

 A B X Y = A.B 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 1

## AND gate using NOR gate

To produce AND gate using NOR gate, the two output of the NOT gates (made from NOR gate by joining the two inputs) are connected to the NOR gate as shown in fig. 5.

The truth table of the above combination is given below.

 A B X Z Y = A.B 0 0 1 1 0 0 1 1 0 0 1 0 0 1 0 1 1 0 0 1

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