The Mathematical Symbol "Xor (⊻)"
The ⊻ Symbol in Mathematics and Logic: Representing Xor
In the realm of mathematical and logical symbols, the ⊻ symbol stands for the "Xor" operation, also known as "exclusive or". Predominantly used in logic and computer science, it signifies a specific kind of disjunction. This article will explore the primary applications of the ⊻ symbol, accompanied by illustrative examples.
Usage
The ⊻ symbol is employed to denote the exclusive or (Xor) operation. The Xor operation yields a true result when there is an odd number of true operands. In simpler terms, for two operands, it returns true if one of them is true and the other is false.
Examples
- Example 1: Consider two logical statements \( p \) and \( q \). Using the ⊻ symbol, the Xor operation can be represented as:
\( p ⊻ q \)
This operation will only be true if \( p \) is true and \( q \) is false, or vice versa. - Example 2: In binary arithmetic (used in computer science), the Xor operation plays a vital role. Let's take two binary numbers: 1101 and 1011. Performing the Xor operation on them bit by bit, we get:
0110
This is because, for each bit position, the result is 1 if the bits are different and 0 if they are the same.
In summary, the ⊻ symbol is of paramount importance in both logic and computer science, allowing for the representation of the Xor operation. This operation is foundational in various logical computations and digital circuit designs, showcasing its wide-ranging applications and significance.
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Codes for the ⊻ Symbol
| The Symbol | ⊻ | |
| Alt Code | Alt 8891 | |
| HTML Code | ⊻ | |
| HTML Entity | ⊻ | |
| CSS Code | \22BB | |
| Hex Code | ⊻ | |
| Unicode | U+22BB |
How To Insert the ⊻ Symbol
(Method 1) Copy and paste the symbol.
The easiest way to get the ⊻ symbol is to copy and paste it into your document.Bear in mind that this is a UTF-8 encoded character. It must be encoded as UTF-8 at all stages (copying, replacing, editing, pasting), otherwise it will render as random characters or the dreaded �.
(Method 2) Use the "Alt Code."
If you have a keyboard with a numeric pad, you can use this method. Simply hold down the Alt key and type 8891. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)(Method 3) Use the HTML Decimal Code (for webpages).
| HTML Text | Output |
|---|---|
| <b>My symbol: ⊻</b> | My symbol: ⊻ |
(Method 4) Use the HTML Entity Code (for webpages).
| HTML Text | Output |
|---|---|
| <b>My symbol: ⊻</b> | My symbol: ⊻ |
(Method 5) Use the CSS Code (for webpages).
| CSS and HTML Text | Output |
|---|---|
|
<style> span:after { content: "\22BB";} </style> <span>My symbol:</span> | My symbol: ⊻ |
(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).
| HTML Text | Output |
|---|---|
| <b>My symbol: ⊻</b> | My symbol: ⊻ |
| JavaScript Text |
|---|
|
const x = "0x"+"E9" ctx.fillText(String.fromCodePoint(x), 5, 5); |
| Output |
⊻ |
(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).
The Unicode for ⊻ is U+22BB. The important part is the hexadecimal number after the U+, which is used in various formats. For example, in Microsoft Office applications (e.g. Word, PowerPoint), do the following:| Type | Output |
|---|---|
| 22BB [Hold down Alt] [Press x] | ⊻ (The 22BB turns into ⊻. Note that you can omit any leading zeros.) |
| JavaScript Text | Output |
|---|---|
| let str = "\u22BB" document.write("My symbol: " + str) | My symbol: ⊻ |