# Logic Gates – All You Need To Know About Them

Find out all about Logic Gates in detail along with their history, working and the use in the modern era. Different types of logic gates are also illustrated.

## History of the Logic Gates

Before the invention of the digital logic gates, the whole concept was based on the mechanical logic gates. In 1837, the scientist Charles Babbage formulated/designed the Analytical Engine. In that engine, all the operations of the logic gates relied on the mechanical gearing. After this invention, in 1891, Almon Strowger has designed the device which contains the logic gate switch circuit. But this concept was not in widespread use. After all these inventions, Claude E. Shannon, in 1937, has developed the concept of the use of the Boolean algebra and has also designed the switching circuits. The first modern electronic AND gate was introduced by the Walther Bothe in 1924. For his great invention, he was awarded the Nobel Prize in physics in 1954. Now, active research is going on for the introduction of the molecular logic gates.

## Introduction to the Logic Gates

It is said that the digital systems are constructed using the logic gates. These gates are the heart of digital electronics. It is the electronic device which helps us to calculate the function of the two-valued signal.

We can define the ‘Logic Gate’ as the idealized electronic device which executes the Boolean function. It is the building block of the digital circuits. These gates are executed using the diodes, transistors etc. They can also be constructed using vacuum tubes, optics, mechanical elements etc. These gates work using the logic circuits which acts like a switch having an ON and OFF state. The fundamental unit of storing the data in the computers is binary digits. Just like the switch, the binary digits have the two states, i.e., 0 and 1, where ‘0’ represents the ‘OFF’ state, and ‘1’ represents the ‘ON’ state. While performing the calculations, these bits are manipulated by the logical operation, which takes the input and gives out the output. This output is given in terms of the combinations of the inputs which are represented to us by using the truth table.

As the electronic logic gates execute the Boolean functions, so it is very important to understand some of the following points:

• Electronic gates should be provided with the proper power supply.
• Inputs are operated using the voltages having the two nominal values.
• The output of a gate should also be given out by the two nominal values of the voltage only.
• There should be an accurate time delay between the input applied and the output that is given out.

Logic Gates are basically, the small transistor circuit (a type of the amplifier) which executes in the different forms within an integrated circuit. They have one or more inputs and gives out only one output. The main concept of the operation is that the circuit runs on the two voltage levels, i.e., logic 0 and logic 1.

## Types of the Logic Gates

Basically, Logic Gates are classified into its seven types

OR gate, AND gate, NOR gate, NAND gate, NOT gate, XNOR gate, XOR gate.

The functions of these logic gates are represented using the truth table. Except for NOT gate (which have only one output), all the other logic gates have two inputs. The truth table is drawn using binary values, i.e., 0 and 1. All the possible combinations depend upon the number of the inputs that we enter in them. The working of all the digital electronics is based upon these seven basic logic gates. The logic rules of the logic gates are described in the different ways, by a truth table or by Boolean algebra.

Now, let us study the detailed information about these basic seven logic gates.

### 1. OR GATE

The OR gate is the digital logic gate having two or more inputs and gives out only one output which performs the logical disjunction. In this logic gate, the output will result truly when at least one of the inputs is true (other input may or may not be true). If all of the inputs are false, then the resultant output of the OR logic gate will also be false. The working of this logic gate can be understood through its truth table

 INPUT A INPUT B OUTPUT True True True True False True False True True False False False

Using binary values, the truth table can be drawn as

 INPUT A INPUT B OUTPUT 1 1 1 1 0 1 0 1 1 0 0 0

The expression for the OR logic gate is Q= A OR B, A + B.

SYMBOLS

There are two commonly used symbols for the OR logic gate.

• The American symbol (ANSI) • The IEC symbol ANALYTICAL REPRESENTATION

The analytical representation of the OR logic gate is

f (a, b)= a + b – a*b

• f (0, 0)= 0 + 0 – 0*0 = 0
• f (0,1)= 0+1 – 0*1 = 1
• f(1,0)= 1+ 0 – 1*0 = 1
• f (1, 1)= 1+1 – 1*1 = 1

### 2. AND GATE

The AND gate is the digital logic gate having two or more inputs and gives out only one output which performs the logical conjunction. In this logic gate, the output will only be true when all the inputs entered will be true. If any of the input is false, then it will result in the false output. Let’s understand the operation of this logic gate using the truth tables

 INPUT A INPUT B OUTPUT True True True True False False False True False False False False

Using the binary values, the truth table can be drawn as

 INPUT A INPUT B OUTPUT 1 1 1 1 0 0 0 1 0 0 0 0

The expression for the AND logic gate is Q = A AND B, A.B, A^B.

SYMBOL

There are two commonly used symbols for the AND logic gate.

• The American symbol (ANSI) • The IEC symbol ANALYTICAL REPRESENTATION

The analytical representation of the AND logic gate is as

f (a , b) = a * b.

• f (0 , 0) = 0*0 = 0
• f (0 , 1) = 0*1 = 0
• f (1 , 0) = 1*0 = 0
• f (1 , 1) = 1*1 = 1

### 3. NOT GATE

For the beginners, it is better to start with the NOT logic gate because it has only one input which in return gives only one output. This gate is also known as the inverter because it performs the logical negation of the input provided to it. If the input provided to the NOT gate is true, then the output given will be false.

Therefore, we can say that inverting NOT logic gates are the single input device. The output from this gate will only be HIGH when the input provided to it will be at the logic level ‘0’(i.e., LOW input).

The Boolean expression for the NOT logic gate is A = Q.

“If A is NOT true, then Q will be true”.

Now, let us see the truth table of the NOT gate.

 INPUT OUTPUT True False False True

Now, we will discuss the two types of logic gates.

• TRANSISTOR NOT GATE. The two input NOT gate can be constructed using the RTL switches where the input is directly connected to the transistor base. The transistor should be in the ‘ON’ state so that we can receive an inverted output, i.e., ‘OFF’ state.
• LOGIC NOT GATE. These are used in the digital circuits where we have to produce the required logical operation/function. In this gate, the symbol is triangular pointing at the right side and has a small bubble at its end. This bubble denotes the inversion of the signal coming to it. This bubbles are not only restricted to the NOT gate but are also present in the digital circuits with the operation of the inversion.

Symbols

There are two commonly used symbols for the NOT logic gate.

• The American symbol (ANSI) • The IEC symbol ANALYTICAL REPRESENTATION

The analytical representation of the NOT logic gate is

f (a) = 1-a.

• f (0) = 1-0 = 1
• f (1) = 1-1 = 0

### 4. NOR GATE

It is the digital logic gate having two or more inputs, and in return, it gives only one output in which it shows the behaviour totally opposite to that of the OR logic gate. It will give the true output only when both the inputs provided to it is false. This can be understood by its truth table

 INPUT A INPUT B OUTPUT True True False True False False False True False False False True

Using binary values, the truth table can be drawn as

 INPUT A INPUT B OUTPUT 1 1 0 1 0 0 0 1 0 0 0 1

It is the combination of the OR gate and the NOT gate.

Now, we will see the two types of the NOR logic gates.

• TRANSISTOR NOR GATE. The two-input NOR gate can be constructed using the RTL switches which are connected together, and the inputs are directly connected to the transistor bases. The transistors should be in the cut off ‘OFF’ state so that we can get the output as Q.
• LOGIC NOR GATES. This gate is used in the digital circuit to produce the required logical operations/functions. Its symbol has the shape same as that of the OR logic gate with an inversion bubble at its output position.

SYMBOLSIt has two commonly used symbols, i.e.,

• The American symbol (ANSI) • The IEC symbol ### 5. NAND gate

It is a logic gate having two or more inputs and gives only one output in return in which it shows the behaviour totally opposite to that of AND gate. When both the values of the input are true, then the output given will be false. Otherwise, in all the other cases, the value of the output is true, i.e., 1. This can be understood using the truth table

 INPUT A INPUT B OUTPUT 1 1 0 1 0 1 0 1 1 0 0 1

NAND gate is the combination of the NOT gate and the AND gate.

Now we will discuss the two types of the NAND gate.

• Transistor NAND gate two-input NAND gate can be constructed using The R-T switches are connected together with the input which is further directly connected to the transistor bases. Either of the transistors should be in the ‘OFF’ state to get the Q output. i.e., if both the inputs A and B are TRUE, then the output Q will be FALSE.
• Logic NAND gate is used in the digital circuits to perform the required logical functions. It has the symbol whose shape s same as that of the AND gate with an inversion bubble at its output which represents the NOT gate symbol.

SYMBOLS

There are two commonly used symbols, i.e.,

• The American symbol • The IEC symbol ### 6. XOR Gate

The XOR gate stands for the exclusive OR gate. It is the digital logic gate which has two or more inputs and gives out only one output. The output of this gate will only be TRUE when only one value of the input given to it is TRUE. If both the values of the input are FALSE or TRUE, then the output will be FALSE. The truth table of this gate is as follows

 INPUT A INPUT B OUTPUT True True False True False True False True True False False False

SYMBOLS

There are two commonly used symbols

• The American symbol (ANSI) • The IEC symbol ANALYTICAL REPRESENTATION

f (a , b) =a + b – 2 * a * a

• f (0,0) = 0 +0 – 2 * 0 * 0 = 0
• f (0 ,1) = 0 + 1 – 2 * 0* 1 = 1
• f (1 , 0) = 1 + 0 – 2 * 1 * 0 = 1
• f (1 , 1) = 1 + 1 – 2 * 1 * 1 = 0

### 7. XNOR Gate

It is the digital logic gate which has two or more inputs and gives out only one output that performs logical equality. XNOR gate stands for the Exclusive XOR gate. It is the combination of the NOT gate and the XOR gate. This gate is also known as the Equivalence gate. The truth table for the XNOR gate is

 INPUT A INPUT B OUTPUT 1 1 1 1 0 0 0 1 0 0 0 1

The symbol for the XNOR gate is the same as that of XOR gate with complement sign added to it.

Symbols It has commonly two symbols

• The American symbol (ANSI) • The IEC symbol ## Applications of the Logic Gates

1. OR GATE. It is used at the point where the occurrence of more than one event is required to detect or some actions that will be performed after their occurrence.
2. AND GATE. It has two main applications that are Enable gate and Inhibit gate. Enable gate allows the data through any channel and the Inhibit gate disallows the data through any channel.
3. NOT GATE. As it is an inverter as it inverts the output signal and shows the reverse result. The CMOS inverters are used because they build up the square wave oscillators that are used in generating the clock signals.
4. NOR GATE. It is used to make the XOR gate. It has some real-time applications, i.e., it is used in the mixer tanks. In the mixer tank, a 3-input NOR gate is used to control the ingredients that are flowing in this tank.
5. NAND GATE. It has two common applications, i.e., used in the burglar alarm and in freezer warning buzzer.
• IN BURGLAR ALARM. When the switch is OFF, the input of the NAND gate will be LOW and when the LDR is in the light, then the second input will be LOW. This means when the switch is OFF, and the light is ON, the input will remain LOW, the resultant output will be HIGH, and the buzzer sounds on.
• FREEZER WARNING BUZZER. In this when the thermistor will be COLD, the resistance will be HIGH, and hence, the input will be HIGH. Since the NAND gate is the inverter gate so its output will be LOW, when the thermistor warms up, then the resistance will decrease, which will result in the fall of the input. When the input becomes LOW enough, then the output becomes HIGH, and the buzzer sounds.
1. XOR GATE.
• They are used for the arithmetic operations because it gives the sum of the two or more binary numbers and hence used in many arithmetic circuits.
• They are used as Controlled inverter.
• It is used to convert the binary code to the grey code or the grey code to the binary code.
• It is used to minimize the combinational logic circuits.
• They are used as a digital comparator.
1. XNOR GATE. It is used to detect the errors in the circuit, which further detects the odd and even parity bits in the digital data transmission circuits. It is commonly used for the encryption and arithmetic circuits.

## UNIVERSAL LOGIC GATES

Universal logic gates are defined as those logic gates which can implement the Boolean function without requiring any other kind of the gate. Among the seven basic logic gates, we have two universal logic gates that are NAND and NOR gates.

They are called so because they can perceive all the binary operations and almost every logic gate can be derived from these two gates.

The universal gates have some special kind of properties –

• They are not associative.
• They are not commutative.

Now, the main point arises is that why NAND and NOT gates are called the universal logic gates?

The answer for the above question is that the NAND gate and the NOR gate can perform all the logical operations of the basic logic gates (OR, AND, NOR, XOR, XNOR). The combination of these two gates is used to accomplish all the basic operations and can also produce the inverter, which the other gates cannot do. This inverting property of the NAND gate and the NOR gate is very useful. The logic gates like OR, AND, XOR etc. cannot act as the universal gate because they are the non- inverting gates which don’t have this versatility.

## THREE STATE LOGIC GATES

It is defined as the logic gate, which gives out the three different types of output LOW (L), HIGH (H) and HIGH IMPEDANCE (Z). The third output (high impedance) does not play any role in the logic and is strictly bound to the binary. These are used in the devices in which the multiple chips allow to send the data. EXAMPLE- used in the buses of the CPU.

In digital electronics, the high output is the souring current from the positive voltage (positive terminal), and the low output is sinking current to the zero voltage (negative terminal). If there will be high impedance, then the output will be effectively disconnected from the circuit.

## Advantages of the logic gates

• performs the logical operations using the Boolean Algebra.
• Logic 0 and logic one can be distinguished easily.
• Acts as the building blocks for any digital device.
• They are cheap. Hence, they become quite cost-efficient.
• Requires less power.

## Disadvantages of the logic gates

• Have a low operating voltage.
• Time delay occurs between the input and the output.

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