Digital Electronics is an essential part of modern-day electronics and communication systems. Digital Systems are made of Digital Logic Circuits that work on binary numbers i.e., 0 and 1. To build those logic circuits, we make use of Logic Gates, which act as a building block of combinational logic circuits. In this article, we will explore some of the basic Logic Gates, checkout their Logic Symbols and truth tables.
Introduction to Logic Gates
Logic Gates are the basic electronic circuits that are used to implement Boolean Expressions (particularly, the two-valued Boolean Expressions). They provide a way to combine and manipulate digital signals based on the laws of Boolean Algebra.
Mathematically, we can use Boolean algebra to work on binary numbers and simplify the logic expressions. But coming to actual implementation in digital systems, we use simple electronic circuits called Logic Gates.
Here are some of the basic Logic Gates that are used to build digital logic circuits.
- OR
- AND
- NOT (Inverter)
- Buffer
- NAND
- NOR
- Exclusive OR (XOR)
- Exclusive NOR (XNOR)
Let us see in detail about these logic gates, take a look at their logic symbols, and also build their truth tables.
Logic Symbols and Truth Tables of Logic Gates
NOT Gate
The NOT logic gate has one input and one output where the output is a complement to the input. If the input is 0 (LOW), then the output of NOT gate is 1 (HIGH) and if the input is 1 (HIGH), the output of NOT gate is 0 (LOW).
As the output of the NOT gate is a complement of the input, it is also called Inverting or Complementing Circuit (gate).
If A is the input to the NOT gate and Y is its output, then the logic equation of NOT gate is Y = .
The Logic Symbol and Truth Table of NOT gate are given below.
Image
| Input (A) | Output (Y = A) |
| 0 | 1 |
| 1 | 0 |
OR Gate
The OR Gate is a two-input logic gate that performs Boolean OR operation on its inputs. The output of the OR Gate is 0 (LOW) only if both the inputs are 0 (LOW). For all other combinations of the inputs, the output of OR Gate is 1 (HIGH).
If A and B are the inputs of an OR Gate and Y is its output, then the logic expression of OR Gate is Y = A + B and it is read as “Y is equal to A OR B”.
The Logic Symbol and Truth Table of the OR gate are given below.
Image
| Input (A) | Input (B) | Output (Y =A+B) |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
AND Gate
The AND Gate is a two-input logic gate that performs Boolean AND operation on its inputs. The output of the AND gate is 1 (HIGH) only if both of its inputs are 1 (HIGH). For all other cases, the output of AND gate is 0 (LOW).
If A and B are the inputs of AND gate and Y is its output, then the logic expression of AND gate is Y = A ‧ B and it is read as “Y is equal to A AND B”.
The Logic Symbol and Truth Table of AND gate are given below.
Image
| Input (A) | Input (B) | Output (Y=A‧B) |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
XOR Gate
The Exclusive OR Gate, which is usually written as XOR Gate or EX-OR Gate, is a two-input logic gate that performs an exclusive OR operation on its inputs. The output of XOR Gate is 1 (HIGH) if the inputs are dissimilar i.e. if one input is 1 (HIGH) and the other input is 0 (LOW). If both the inputs are the same i.e., both are 1 (HIGH) or both are 0 (LOW), then the output of XOR Gate is 0 (LOW).
If A and B are the inputs of an XOR Gate and Y is its output, then the logic expression of the XOR gate is Y = AB + AB or Y = A ⊕ B.
The Logic Symbol and Truth Table of the XOR gate are given below.
Image
| Input (A) | Input (B) | Output (Y=A⊕B) |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Buffer
A Buffer is an interesting circuit that doesn’t do any logical operation but rather acts as a signal amplifier. The output of the buffer is the same as the input and it acts as a transfer function.
Usually, buffers are available as Tri-State Buffers, which have an additional ‘Enable’ input. When Enable (E) input is 0 (LOW), the output is in a high-impedance state and when the Enable (E) input is 1 (HIGH), the output follows the input i.e., same as the input.
Internally, buffers are configured as two NOT gates connected back-to-back.
The Logic Symbol and Truth Table of Buffer is given below.
Image
| Input (A) | Output (Y=A) |
| 0 | 0 |
| 1 | 1 |
NAND Gate
The next two gates are known as Universal Gates. In that, the first one is the NAND Gate. It stands for NOT AND Gate i.e., an AND Gate followed by a NOT Gate. The output of NAND is the complement of AND Gate i.e., the output of NAND Gate is 0 (LOW) only if both the inputs are 1 (HIGH). In all the other cases, its output is 1 (HIGH).
If A and B are the inputs of the NAND Gate and Y is its output, then the logic expression of the NAND gate is Y =A ‧ B.
The Logic Symbol and Truth Table of the NAND gate are given below.
Image
| Input (A) | Input (B) | Output (Y=A ‧ B) |
| 0 | 0 | 1 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
NOR Gate
Just like AND has NAND, the OR gate has NOR Gate. It stands for NOT OR Gate and as expected it is an OR Gate followed by a NOT Gate. The output of NOR Gate is 1 (HIGH) if and only if both its inputs are 0 (LOW). In all other combinations of inputs, the output of NOR Gate is 0 (LOW).
If A and B are the inputs of NOR Gate and Y is its output, then the logic expression of NOR Gate is Y=A + B.
The Logic Symbol and Truth Table of the NOR gate are given below.
Image
| Input (A) | Input (B) | Output (Y=A + B) |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
XNOR Gate
The last important logic gate is the Exclusive NOR Gate. It is usually written as EX-NOR or XNOR Gate. It is equivalent to an XOR gate followed by a NOT gate. The output of XNOR Gate is 1 (HIGH) if both of its inputs are the same i.e., both the inputs are either 0 (LOW) or 1 (HIGH). If the inputs of XNOR Gate are dissimilar, then its output is 0 (LOW).
If A and B are the inputs to XNOR Gate and Y is its output, then the logic expression of XNOR Gate is Y = A ⊕ B.
The Logic Symbol and Truth Table of the NOR gate are given below.
Image
| Input (A) | Input (B) | Output (Y=A ⊕ B) |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Logic Symbols Chart
We have seen all the important and basic logic gates along with their logic expressions, symbols, and truth tables. Here is a chart that consists of the logic symbols and truth tables of all the 8 logic gates discussed above.
Image
Conclusion
We have seen the basics of Logic Gates including NOT, OR, AND, NAND, NOR, XOR, XNOR, and Buffer along with their logic expressions, logic symbols, and truth tables. Logic Symbols are very useful in the schematic representation of Logic Gates.
