# Logic gates | logic gates pdf | logic gates truth table | logic gates symbols | Bteup Syllabus 2021-2022 electronic Engineering

**Logic gates | logic gates pdf | logic gates truth table | logic gates definition | logic gates symbols | logic gates in computer **

**Logic Gates**

**Logic gates** play an important role in circuit design and digital systems. It is a building block of a digital system and an electronic circuit that always have only one output. These gates can have one input or more than one input, but most of the gates have two inputs. On the basis of the relationship between the input and the output, these gates are named as AND gate, OR gate, NOT gate, etc.

There are different types of gates which are as follows:

## AND Gate

This gate works in the same way as the logical operator "and". The AND gate is a circuit that performs the AND operation of the inputs. This gate has a minimum of 2 input values and an output value.

Y=A AND B AND C AND D……N

Y=A.B.C.D……N

Y=ABCD……N

### Logic Design

### Truth Table

## OR Gate

This gate works in the same way as the logical operator "or". The OR gate is a circuit which performs the OR operation of the inputs. This gate also has a minimum of 2 input values and an output value.

Y=A OR B OR C OR D……N

Y=A+B+C+D……N

### Logic Design

### Truth Table

## NOT Gate

The NOT gate is also called an inverter. This gate gives the inverse value of the input value as a result. This gate has only one input and one output value.

Y=NOT A

Y=A'

### Logic Design

### Truth Table

## NAND Gate

The NAND gate is the combination of AND gate and NOT gate. This gate gives the same result as a NOT-AND operation. This gate can have two or more than two input values and only one output value.

Y=A NOT AND B NOT AND C NOT AND D……N

Y=A NAND B NAND C NAND D……N

### Logic Design

### Truth Table

## NOR Gate

The NOR gate is the combination of an OR gate and NOT gate. This gate gives the same result as the NOT-OR operation. This gate can have two or more than two input values and only one output value.

Y=A NOT OR B NOT OR C NOT OR D……N

Y=A NOR B NOR C NOR D……N

### Logic Design

### Truth Table

## XOR Gate

The XOR gate is also known as the Ex-OR gate. The XOR gate is used in half and full adder and subtractor. The exclusive-OR gate is sometimes called as EX-OR and X-OR gate. This gate can have two or more than two input values and only one output value.

Y=A XOR B XOR C XOR D……N

Y=A⨁B⨁C⨁D……N

Y=AB'+A'B

### Logic Design

### Truth Table

## XNOR Gate

The XNOR gate is also known as the Ex-NOR gate. The XNOR gate is used in half and full adder and subtractor. The exclusive-NOR gate is sometimes called as EX-NOR and X-NOR gate. This gate can have two or more than two input values and only one output value.

Y=A XNOR B XNOR C XNOR D……N

Y=A⊖B⊖C⊖D……N

Y=A'B'+AB

### Logic Design

### Truth Table

# AND Gate

The AND gate plays an important role in the digital logic circuit. The output state of the AND gate will always be low when any of the inputs states is low. Simply, if any input value in the AND gate is set to 0, then it will always return low output(0).

The logic or Boolean expression for the AND gate is the logical multiplication of inputs denoted by a full stop or a single dot as

A.B=Y

The value of Y will be true when both the inputs A and B are set to true.

## Types of Digital Logic AND Gate

The AND gate is classified into three types based on the input it takes. These are the following types of AND gate:

### The 2-input AND Gate

This is the simple formation of the AND gate. In this type of AND gate, there are only two input values and an output value. There are 2^{2}=4 possible combinations of inputs. The truth table and logic design are given below:

Logic Design

Truth Table

### The 3-input AND Gate

Unlike 2-input AND gate, the 3-input AND gate have three inputs. The Boolean expression of the logic AND gate is defined as the binary operation dot(.). The AND gate can be cascaded together to form any number of individual inputs. There are 2^{3}=8 possible combinations of inputs. The truth table and logic design is given below:

Logic Design

Truth Table

### The Multi-input AND Gate

In digital electronics, we can form n-input AND gate also. If there are n inputs, then (N/2)+1 AND gates will be used.

For example:

If we have 6 inputs A, B, C. D, E, F, then 4 AND gates are used in the logic design of 6-input AND gate. There is the following expression of the 6-input AND gate:

Y=(A.B).(C.D).(E.F)

In simple words, it is expressed as:

Y=A AND B AND C AND D AND E AND F

Logic Design

Truth Table

# OR Gate

The OR gate is a mostly used digital logic circuit. The output state of the OR gate will always be low when both of the inputs states is low. Simply, if any input value in the OR gate is set to 1, then it will always return high-level output(1).

The logic or Boolean expression for the OR gate is the logical addition of inputs denoted by plus sign(+) as

A+B=Y

The value of Y will be true when one of the inputs is set to true.

## Types of Digital Logic AND Gate

Just like AND gate, the OR gate is also classified into three types based on the input it takes. These are the following types of OR gate:

### The 2-input OR gate

This is the simple form of the OR gate. In this type of OR gate, there are only two input values and an output value. There are 2^{2}=4 possible combinations of inputs. The truth table and logic design are given below:

Logic Design

Truth Table

### The 3-input OR gate

Just like AND gate, the OR gate can also have any number of individual inputs. The Boolean expression of the logical OR gate is defined as the binary operation plus(+). Like AND gate, OR gate can also be cascaded together to form any number of individual inputs. There are 2^{3}=8 possible combinations of inputs. The truth table and logic design are given below:

Logic Design

Truth Table

### The Multi-input OR Gate

The n-input OR gate can also be formed. If there are n inputs, then (N/2)+1 OR gates will be used

For example:

If we have 6 inputs A, B, C. D, E, F, then 4 OR gates are used in the logic design of the 6-input OR gate. There is the following expression of the 6-input OR gate:

Y=(A+B)+(C+D)+(E+F)

In simple words, it is expressed as:

Y=A OR B OR C OR D OR E OR F

Logic Design

Truth Table

# NOT Gate

The NOT gate is the most basic logic gate of all other logic gates. NOT gate is also known as an inverter or an inverting Buffer. NOT gate only has one input and one output. When the input signal is "Low", the output signal is "High" and when the input signal is "High", the output is "Low". The Boolean expression for the NOT gate is as follows:

A'=Y

When A is not true,then Y is true

The standard NOT gate is given a symbol that is shaped like a triangle with a circle at the end, pointing to the right. This circle is known as an "invert bubble" and is used to represent the logical operation of the NOT function in the NOT, NAND and NOR symbols in their output.

### Logic Design

### Truth Table

The complement value is generated by the NOT gate. The NOT gate is so-called because when the input signal is 0, the output signal will NOT be 0, Similarly, when the input signal is 1, the output signal will NOT be 1.

In the NOT gate, the bubble denotes the single inversion of the output signal. But this bubble can also exist on the gate's input to indicate an active-less input. This reversal of the input signal is not limited only to the NOT gate, but can also be used on any digital circuit or gate, as shown with the operation of inversion, whether it is at the input or output terminals. The easiest way is to think of the bubble as an inverter.

## Use of Active-low Input Bubble

## Equivalent Gates

The **NOT gate** can also be formed with the help of the universal gates, i.e., NAND and NOR. For this, we have to connect both the inputs together to a common input signal. The NOT gate representation of NAND and NOR gate is as follows:

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