XOR Gate – Definition, Explanation, Truth Table and Analogy
An XOR, or Exclusive OR gate, is a fundamental digital logic gate that operates on binary inputs and produces a binary output based on the exclusive disjunction (XOR) operation. Let us learn more about XOR logic gate, its truth table and its explanation in our blog.
Definition of XOR: “XOR” is the abbreviation for “Exclusively-OR.” It is a logical operator that performs a specific operation on its input signals, producing a corresponding output signal. The simplest XOR gate is a two-input digital circuit.
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XOR Gate Truth Table
| Input A | Input B | Output |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Here is a simple explanation of the XOR truth table –
- If both inputs are “0” (same inputs), the output is “0”.
- When one input is “0” and the other is “1” (different inputs), the output is “1”.
- When both inputs are “1” (same inputs), the output is “0”.
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XOR Gate Boolean expression
In Boolean algebra, the XOR operation is also known as the exclusive disjunction. The Boolean expression for an XOR gate can be represented using the “+” symbol to denote the XOR operation.
The XOR gate takes two binary inputs (A and B) and produces a single output (X). The Boolean expression for an XOR gate is as follows:
Q = A ⊕ B
Here’s a breakdown of the expression:
- “Q” represents the output of the XOR gates.
- “A” and “B” are the two input values.
The symbol “⊕” denotes the XOR operation. This operation estimates true (1) when the inputs are different and false (0) when the inputs are the same.
XOR Gates Configurations
There are two main configurations of XOR gates based on the number of inputs:
2-Input XOR gate
The 2-Input Ex-OR gate is the most basic type of XOR gate –
In this truth table:
- “A” and “B” are the two binary input values.
- “Q” represents the XOR gate’s output based on the inputs.
The XOR evaluates to true (1) when the inputs are different and false (0) when the inputs are the same. To understand it better, here is the representation of its evaluation –
0 ⊕ 0 = 0
0 ⊕ 1 = 1
1 ⊕ 0 = 1
1 ⊕ 1 = 0
3-Input XOR gate
A 3-input XOR gate takes three binary inputs and produces a single output. The XOR operation evaluates to true (1) when an odd number of inputs are true (1), and false (0) otherwise.
The 3-input XOR gate follows the same logic but with three input signals.
The truth table for a 3-input XOR gate is as follows:
| A | B | C | Output (Q) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 |
In this truth table:
- “A,” “B,” and “C” are the three binary input values.
- “Q” represents the XOR gate’s output based on the inputs.
The XOR operation evaluates to true (1) when an odd number of inputs are true (1). Please note that the “Output” column has a value of 1 when the number of true inputs (1s) is odd and 0 in case the number of true inputs is even.
Analogy: Food Combinations and the XOR Logic Gate
Imagine you want to make some unique food combinations, but you have two ingredients in front of you: chocolate and vanilla ice cream.
- Putting two scoops of chocolate ice cream together is still chocolate ice cream (output: 0). The taste doesn’t change because you used the same ingredient.
- But suppose you take a scoop of chocolate ice cream and a scoop of vanilla ice cream and combine them. In that case, you’ve created something new – a swirl of different and exciting flavours (output: 1). Combining different ingredients results in a new flavour.
Technical inference to the XOR gates:
- The XOR gate is like your food adventure. It takes two inputs, just like the two ice cream flavours.
- If the inputs are the same (both 0 or both 1), the XOR gate’s output is 0. It’s like mixing the same ice cream flavours – you get nothing new.
- But if the inputs are different (one 0 and one 1), the XOR gate’s output is 1. Like mixing chocolate and vanilla ice cream to create a unique taste, the XOR gate combines inputs to create a special result.
Comparison Table of XOR, AND, OR, and NAND Gates
| Feature |
XOR Gate |
AND Gate |
OR Gate |
NAND Gate |
| Definition |
Outputs 1 when inputs are different, 0 when inputs are the same. |
Outputs 1 only when all inputs are 1. |
Outputs 1 when at least one input is 1. |
Outputs the opposite of AND gate (NOT AND). Produces 0 only when all inputs are 1. |
| Truth Table Output |
0, 1, 1, 0 |
0, 0, 0, 1 |
0, 1, 1, 1 |
1, 1, 1, 0 |
| Key Function |
Detects differences between inputs. |
Requires all inputs to be true for a positive output. |
Allows any input to be true for a positive output. |
Inverts the AND gate’s output. |
| Use Case |
Useful for comparing two inputs, like checking if two data bits are different, which is handy for detecting errors in data transmission. |
Requiring multiple security checks to be cleared before granting access |
Turning on a light if either of two switches is flipped. |
Universal gate used to build any logic circuit, a versatile building block for digital circuits. |
| Symbol |
⊕ |
∧ |
∨ |
NAND |
Conclusion
The XOR gate is a fundamental component in digital logic, widely used in circuits that require comparison, error detection, and encryption. Its unique property of producing a high (1) output only when inputs differ makes it essential for applications like binary addition, parity checking, and cryptographic systems.
Understanding XOR gates, their truth tables, Boolean expressions, and practical uses helps build more complex digital systems. Whether in computer processors, data transmission, or arithmetic logic units (ALUs), XOR remains a crucial element of digital electronics. Mastering XOR operations can enhance their knowledge of logic gates and improve their ability to design efficient and optimized circuits.
FAQs
What are the applications of XOR gates?
XOR gates are used in various applications such as error detection and correction, digital communication, cryptography, binary arithmetic, and designing complex logic circuits.
How is an XOR gate used in cryptography?
XOR gates are used in cryptographic algorithms to encrypt and decrypt data. When data is XORed with a secret key, it becomes encrypted. XORing the encrypted data with the same key decrypts it.
How is an XOR gate symbol represented in circuit diagrams?
An XOR gate is represented by a symbol resembling a plus sign (+) with a small circle at the intersection. The inputs are connected to the ends of the plus sign, and the output comes out from the center of the symbol.
Can XOR gates be combined to create other logic gates?
XOR gates can be combined with other logic gates to create various logic functions. In fact, XOR gates are considered universal, meaning that any logic function can be constructed using only XOR gates.
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