Logic AND Gate

Introduction :

Logic gates are the digital electronics devices (or) circuits, which accepts one (or) more number of inputs, but gives only one number of output.

Why do we need logic gates in the first place? Logic gates are the building blocks for the modern digital computation. With the help from the logic gates, any kind of logic functions can be performed. There are so many different types of logic gates, These are classified depends on their logical operations, ( EX-OR, EX-NOR )among them some are classified as Basic logic gates ( AND, OR, NOT ) and some are classified as Universal logic gates ( NAND, NOR ) . Here the AND logic gate is classified as Basic logic gate. The electronic circuit which performs this AND logic function is called AND logic gate.

Logic gates are the basic building blocks, for all the modern day digital electronics devices.

AND logic gate :

The logic behind the AND logic gate is, “If all the inputs to a logic gate is logic high, then only it’s output is logic high”. These type of logic gate is known as AND logic gate.

What is meant by logic high?

Here logic high means the input voltage of one of the inputs is slightly higher than the input voltage of the other inputs. The most common logic high input voltages are (+5 V, +1 V, +3.3 V etc.,). In digital terms logic high is represented as “1” in positive logic and as “0” in negative logic. In digital terminology “1” is not a mathematical constant one (1), it’s just a representation of logic high state in positive logic, similarly “0” is not a mathematical constant zero (0), it’s just a representation of logic high state in negative logic.

In Boolean algebra term,

logic high = 1 = high voltage ( positive logic )

logic high = 0 = high voltage ( negative logic )

What is meant by logic low?

Here logic low means the input voltage of one of the inputs is slightly lower than the input voltage of the other inputs. The most common logic low input voltages are ( 0 V, -5 V, -3.3 V, -1 V etc.,). In digital terms logic low is represented as “0” in positive logic and as “1” in negative logic. In digital terminology “0” is not a mathematical constant zero (0), it’s just a representation of logic low state in positive logic, similarly “1” is not a mathematical constant one (1), it’s just a representation of logic low state in negative logic.

In Boolean algebra term,

logic low = 0 = low voltage ( positive logic )

logic low = 1 = low voltage ( negative logic )

Note :

1. AND logic is same as the binary multiplication.
2. Any open ended input is treated as logic “1” in Positive logic AND gate.
3. Any open ended input is treated as logic “0” in Negative logic AND gate.

Basic logic gates :

AND gate, OR gate, NOT gate are called as basic logic gates. Why are they called as Basic logic gates?

Any logic function (or) logic gate can be created by using the mixture of AND, OR, NOT logic gates. This is why these gates are called as Basic logic gates.

Ex :

AND operator :

Logical AND operator is represented as “.”, Read it as “AND”. It acts like a binary multiplication.

EX :

Boolean Expression = A . B , Read it as A “AND” B

Classification of logic AND gates :

AND gates are classified depends upon their number of inputs. The most commonly used AND gates are

• Two input logic AND gate.
• Three input logic AND gate.

Two input logic AND gate :

If an AND logic gate, which accepts two inputs and provide the desired AND logic as output then that type of logic gate is called as Two input AND gate.

It’s logic function is,

Positive logic :

“When two inputs are logic high (1), only then the output is logic high (1)”. Positive logic, gates are widely used.

Negative logic :

“When two inputs are logic high (0), only then the output is logic high (0)”.

Logic Symbol :

Switch representation :

If,

n = number of switches (inputs)

m = maximum possible number of output combination

Ex :

number of inputs (n) = 2

Maximum possible number of output combination (m) = 2² = 4

Truth table :

Positive logic :

If any one input is,

0 = AND gate is disabled with output is zero (0).

1 = AND gate is act as a buffer with output is the other input.

With this we can say that,

Positive logic AND gate is equals to the Negative logic OR gate

Unused input :

TTL logic :

In TTL logic, if any input is open (or) floating, it will act as “1”

ECL logic :

In ECL logic, if any input is open (or) floating, it will act as “0”

In positive logic AND gate, the open (or) floating input follows TTL logic, which means open (or) floating input in Positive logic AND gate is considered as “1”.

Negative logic :

If any one input is,

0 = AND gate is act as a buffer with output is the other input.

1 = AND gate is disabled with output is one (1).

With this we can say that,

Negative logic AND gate is equals to the Positive logic OR gate

Unused input :

TTL logic :

In TTL logic, if any input is open (or) floating, it will act as “1”

ECL logic :

In ECL logic, if any input is open (or) floating, it will act as “0”

In negative logic AND gate, the open (or) floating input follows ECL logic, which means open (or) floating input in Negative logic AND gate is considered as “0”.

Three input logic AND gate :

If an AND logic gate, which accepts three inputs and provide the desired AND logic as output then that type of logic gate is called as Three input AND gate.

It’s logic function is,

Positive logic :

“When three inputs are logic high (1), only then the output is logic high (1)”. Positive logic gates are widely used.

Negative logic :

“When three inputs are logic high (0), only then the output is logic high (0)”.

Logic Symbol :

Switch representation :

If,

n = number of switches (inputs)

m = maximum possible number output of combination

Ex:

number of inputs (n) = 3

Maximum possible number of output combination (m) = 2³ = 8

Truth table :

Positive logic :

If any one input is,

0 = AND gate is disabled with output is zero (0).

1 = AND gate gives AND of the other two inputs as output.

With this we can say that,

Positive logic AND gate is equals to the Negative logic OR gate

Unused input :

TTL logic :

In TTL logic, if any input is open (or) floating, it will act as “1”

ECL logic :

In ECL logic, if any input is open (or) floating, it will act as “0”

In positive logic AND gate, the open (or) floating input follows TTL logic, which means open (or) floating input in Positive logic AND gate is considered as “1”.

Negative logic :

If any one input is,

0 = AND gate gives AND of the other two inputs as output.

1 = AND gate is disabled with output is one (1).

With this we can say that,

Negative logic AND gate is equals to the Positive logic OR gate

Unused input :

TTL logic :

In TTL logic, if any input is open (or) floating, it will act as “1”

ECL logic :

In ECL logic, if any input is open (or) floating, it will act as “0”

In negative logic AND gate, the open (or) floating input follows ECL logic, which means open (or) floating input in Negative logic AND gate is considered as “0”.

Boolean law :

AND gate is following all these Boolean laws.

• Commutative law :

This law states that, The binary product of the two inputs is equivalent to the binary product performed by changing the order of the same inputs.

i.e.

where, A & B are logic inputs.

• Associative law :

This law states that, if we have three logic inputs, then the binary product between the binary product of the second and third logic input, to the first logic input, is equal to the binary product between the binary product of the first and second logic input, to the third logic input.

i.e.

where, A,B & C are logic inputs.

• Distributive law :

This law states that, if we have three logic inputs, then the binary addition of the first logic input with the binary product of the second logic input and third logic input is equal to the binary product between the binary addition of the first logic input with the second logic input and the binary addition of the first logic input with the third logic input.

i.e.

where, A,B & C are logic inputs.

Conclusion :

Now we all know, that what is logic AND gate and how it operates. Logic gates are the basic building blocks for any kind of digital electronic devices/systems. AND logic gate is known as Basic logic gate, because with the combination of AND, OR, NOT logic gate, it is possible to make any kind of digital logical functions.