Logic Gate (AND, OR, XOR, NOT, NAND, NOR and XNOR)

Logic Gates are fundamental components in electronics, used to perform logical operations on binary inputs. These gates form the backbone of digital circuits and are primarily based on Boolean Algebra. Logic Gates take one or more binary inputs (0 or 1) and produce a single binary output based on a specific operation. Understanding the different types of basic Logic Gates is essential for anyone studying digital electronics or working with circuits.

What are Logic Gates in Digital Electronics?

In simple terms, logic gates are electronic devices that manipulate binary data. They perform logical operations like AND, OR, and NOT, based on the inputs provided. Logic gates are crucial in the construction of digital circuits and are used in a wide variety of applications, such as computers, calculators, and other electronic devices.

These gates are commonly constructed using transistors and are the building blocks for more complex devices like adders, multiplexers, and flip-flops.

Types of Logic Gates

There are several Types Of Logic Gates, each performing specific logical functions:

• OR Gate

• AND Gate

• NOT Gate

• XOR Gate

Additionally, these gates can be combined in various ways, resulting in other gates like the NAND Gate, NOR Gate, XOR Gate, and XNOR Gate.

1. OR Gate

• Operation: The output of an OR gate is 1 if at least one of its inputs is 1.

• Boolean Expression: Y=A+B

• Truth Table:

2. AND Gate

• Operation: The output of an AND gate is 1 only if all of its inputs are 1.

• Boolean Expression: Y=A⋅B

• Truth Table:

3. NOT Gate (Inverter)

• Operation: The output of a NOT gate is the inverse of the input. If the input is 1, the output will be 0, and vice versa.

• Boolean Expression: $Y=\bar{A}$

• Truth Table:

4. NAND Gate

• Operation: A combination of an AND gate and a NOT gate. The output of a NAND gate is the inverse of the AND gate output.

• Boolean Expression: $Y=\overline{A\cdot B}$

• Truth Table:

5. XOR Gate (Exclusive OR)

• Operation: The output of an XOR gate is 1 if exactly one of its inputs is 1.

• Boolean Expression: $Y=A\oplus B$

• Truth Table:

6. NOR Gate

• Operation: A combination of an OR gate and a NOT gate. The output is the inverse of the OR gate.

• Boolean Expression: $Y=A+B‾Y=\overline{A+B}Y=A+B$​

• Truth Table:

7. XNOR Gate (Exclusive NOR)

• Operation: A combination of an XOR gate and a NOT gate. The output is 1 when both inputs are the same (either both 0 or both 1).

• Boolean Expression: $Y=\overline{A\oplus B}$

• Truth Table:

Applications of Logic Gates

Logic gates are widely used in digital circuits, including:

1. Arithmetic Operations: Used in addition and subtraction operations in computers.

2. Data Storage: Essential in flip-flops and memory devices.

3. Control Systems: Found in traffic lights, alarms, and control systems.

4. Signal Processing: Used in amplifiers and filters.

5. Computers and Digital Devices: The foundation of central processing units (CPUs) and other computer hardware.

De Morgan’s Theorems

De Morgan’s Theorems provide rules for transforming logic gates, specifically NAND and NOR gates:

1. First Theorem:
   $\overline{A\cdot B}=\bar{A}+\bar{B}$
   This shows that a NAND gate is equivalent to a bubbled AND gate.

2. Second Theorem:
   $\overline{A+B}=\bar{A}\cdot \bar{B}$
   This shows that a NOR gate is equivalent to a bubbled OR gate.

Important Logic Gate Conversions

1. The logic diagram of X-NOR gate using NOR gate is given as:

Truth table:

1. X-NOR gate using NAND gate

Truth table: