Logic Gates A Logic Gates is an electronic

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Logic Gates A Logic Gates is an electronic circuit which performs the particular logic

Logic Gates A Logic Gates is an electronic circuit which performs the particular logic operation. They are also known as the building block of the digital electronics circuits. It is a combination of various (one or more than one) input and output. They are built up by various integrated circuits.

 • The integrated circuits are also known as very large scale integrated circuits,

• The integrated circuits are also known as very large scale integrated circuits, larger integrated circuits and small-scale integrated circuits. The inputs and outputs of logic gates can be represented by HIGH and LOW, 0 and 1, True and False.

AND Gate • AND gate also has two or more input signals same as

AND Gate • AND gate also has two or more input signals same as that of the OR gate, and the output is single. The gate has a high output only when all the input signals are high otherwise the output signal is low. The logic symbol for the gate is shown below.

 • The switching circuit of the AND gate is shown below. A lamp

• The switching circuit of the AND gate is shown below. A lamp is connected to a voltage source through the two switches A and B. The lamp will glow when both the switches are closed. If any one of the switches is opened, the lamp will not glow.

 • The truth table of the AND gate is given below: A B

• The truth table of the AND gate is given below: A B Z 0 0 1 1 1 • The output of this gate will be HIGH if all the input signals are high.

OR Gate • An OR gate has two or more than two inputs and

OR Gate • An OR gate has two or more than two inputs and one output signal. It is called an OR gate because the output signal will be high only if any or all input signals are high. • The OR gate follows the logical operation of the input and output signals. It permits the signal to pass and stop through it. The logic symbol for the gate is shown below:

 • The switching circuit of the gate operation is shown below: A lamp

• The switching circuit of the gate operation is shown below: A lamp L is connected to a voltage source. A and B are the two switches. The switching circuit illustrates that the lamp L will glow when either of the switches A or B or both A and B is closed. The lamp will go off when both the switches are in the open condition.

 • The truth table of the gate is given below: A 0 0

• The truth table of the gate is given below: A 0 0 1 1 B 0 1 Z 0 1 1 1 From the truth table, it is clear that, when the inputs of the OR gate are LOW that is 0, the output will be 0. If any one of the inputs or both the inputs of the OR gate is 1 that is HIGH, the output will be high, i. e. , 1.

NOT Gate • The NOT gate is a single input single output gate. This

NOT Gate • The NOT gate is a single input single output gate. This gate is also known as Inverter because it performs the inversion of the applied binary signal, i. e. , it converts 0 into 1 or 1 into 0. • In other words, the gate which has a high input signal only when their input signal is low such type of gate is known as the not gate. The logic symbol for the gate is shown below:

 • The symbol of the not gate is a triangle with a bubble

• The symbol of the not gate is a triangle with a bubble on its end. This bubble is known as the inversion bubble. It gives the complement of the input signal. It is also known as decisionmaking devices because it has only one input. The switching circuit diagram of the NOT gate is shown below:

 • The truth table of the gate is given below: A 0 1

• The truth table of the gate is given below: A 0 1 Z 1 0

NAND Gate • The NAND gate is a combination of an AND gate and

NAND Gate • The NAND gate is a combination of an AND gate and NOT gate. They are connected in cascade form. It is also called Negated And gate. The NAND gate provides the false or low output only when their inputs is high or true. The NAND gate is essential because different types of a boolean function are implemented by using it. • The NAND gate has the property of functional completeness. The function completeness means any types of gates can be implemented by using the NAND gate. It performs the function of OR, NOR and AND gate.

 • The logic symbol for the gate is shown below: The logic circuit

• The logic symbol for the gate is shown below: The logic circuit of the NAND gate is shown below: From the logic circuit, the output can be expressed as:

 • The equation is read as “Z equals NOT A AND B”. Since

• The equation is read as “Z equals NOT A AND B”. Since the logic circuit involves an AND gate followed by an inverter. The output can only be low when both the inputs are high. • The truth table of the NAND gate is given below: A B Z 0 0 1 1 1 0

 • From the truth table of the gate, it is clear that all

• From the truth table of the gate, it is clear that all the inputs must be high to get a low output and if any of the input is low, the output obtained will be high. If any one of the input is also high the output will be high that is 1.

NOR Gate • An OR gate followed by a NOT gate in a cascade

NOR Gate • An OR gate followed by a NOT gate in a cascade is called a NOR gate. In other words, the gate which provides a high output signal only when there are low signals on the inputs such type of gate is known as NOR gate. • The logic symbol of the gate is shown below:

 • The logic circuit of the gate is shown below: From the logic

• The logic circuit of the gate is shown below: From the logic circuit of the NOR gate, the output can be expressed by the equation shown below. The below equation is read as “Z equals NOT A OR B”. Since the logic circuit involves an OR gate followed by an Inverter, the output can only be high when both the inputs are low.

 • The truth table of the NOR gate is given below: A B

• The truth table of the NOR gate is given below: A B Z 0 0 1 0 1 0 0 1 1 0 • Hence, in NOR gate, all the inputs must be low to get high output that is when both the inputs A and B are at 0 the output will be 1. If any of the input is high, the output of the gate will be low that is 0. If both the inputs are high then also, the output will be low, i. e. , 0.

Exclusive OR Gate – EXOR Gate • The EXOR gate is used extensively in

Exclusive OR Gate – EXOR Gate • The EXOR gate is used extensively in digital data processing circuits and is known as Exclusive-ORgate. The EXOR gate has a high output only when an odd number of inputs are high. For the two input EXOR gates, the output will be high when the set of input is either 01 or 10. • The XOR gate is used in the adder, subtractor and controlled inverter circuit. It is also used in the computers for implementing the binary addition.

The logic symbol of the EXOR gate is shown above. The output of an

The logic symbol of the EXOR gate is shown above. The output of an exclusive OR gate will be low for the set of input is either 00 or 11. Therefore, the gate can be used as a Comparator where it gives high output if both the inputs are not equal. The logic circuit of the gate is shown below:

 • The truth table for this logic gate for all set of the

• The truth table for this logic gate for all set of the inputs 00, 01, 10 or 11 is shown below: A 0 0 1 1 • For AB: 00 • For AB: 01 B 0 1 Z 0 1 1 0

 • For AB: 10 • For AB: 11 From the truth table, it

• For AB: 10 • For AB: 11 From the truth table, it is analysed that the output is high when A or B is high, but it is not high when both are high. That’s why this logic circuit is known as an exclusive-OR gate. Thus, the inputs must be different to get high output from the two input exclusive OR gate.

Exclusive NOR Gate – EXNOR Gate • EXNOR gate means exclusive NOR gate and

Exclusive NOR Gate – EXNOR Gate • EXNOR gate means exclusive NOR gate and is a combination of X-OR and NOT gate. It also has two inputs and one output. When both the inputs are at 0, the output of the EXNOR gate will be high i. e. 1. If one of the input is 0 and the other is 1 the output will be 0, and the gate is known as Coincidence gate. • The logical symbol of the gate is shown below:

 • It is also called an inequality detector. The output of the exclusive

• It is also called an inequality detector. The output of the exclusive ex-nor gate is high only when both the inputs of the gate are at the same logic (i. e, both the inputs are either high or low). The output of the gate is high only when both of their inputs are equivalent to each other and because of this the ex-nor gate is known as an equivalent gate. • The logical symbol of exclusive nor gate is represented by the exclusive-or gate with the bubble. It is complementary to the exclusive or gate.

 • The truth table of the gate is given below: A B Z

• The truth table of the gate is given below: A B Z 0 0 1 0 1 0 0 1 1 1 • In general, the output of the logic gate is high only when its inputs are of even numbers and low output is obtained only when its inputs are of odd numbers.