XOR Symbol / Circled Plus
About XOR Symbol / Circled Plus
⊕ is the XOR symbol (exclusive OR symbol), also known as circled plus in mathematics and logic, used to represent the XOR operation where "same is false, different is true". When searching how to type the XOR symbol, the answer is right here.
The ⊕ symbol consists of a plus sign surrounded by a circle, making it a universally recognized logic operator. The XOR symbol plays a core role in digital circuits, cryptography, and programming bitwise operations.
【Operation Rules】The rule of XOR operation is simple: the result is false (0) when both inputs are the same, and true (1) when the inputs are different. This property makes the XOR symbol widely used in data encryption, checksum calculation, and graphics rendering.
【Modern Usage】⊕ is frequently used in programming language bitwise operations (such as ^ in C/Java), digital circuit XOR gate design, cryptographic stream cipher algorithms, CRC checks, and various logical scenarios requiring judgment of "whether they are different".
How to Type XOR Symbol / Circled Plus
Windows Input
Method 1: Hold Alt, type 8853 on the numeric keypad; Method 2: type xor with your input method and select ⊕
Mac Input
Method 1: Press Control + Command + Space to open the character panel, search "circled plus"; Method 2: type xor with your input method and select ⊕
HTML/CSS Input
HTML: ⊕ or ⊕; CSS: content: "\2295";
LaTeX Input
Use \oplus command in math mode; requires the amssymb package. In text mode, you can also use \textcircled{+}
XOR Symbol / Circled Plus FAQ
What is the difference between the XOR symbol ⊕ and the plus sign +?
⊕ is the XOR symbol, following the rule "same is 0, different is 1", not simple arithmetic addition. In binary, 1⊕1=0 (carry discarded), while 1+1=10 (with carry). The regular plus sign + is used for arithmetic, while ⊕ is used for logical and bitwise operations.
How does the XOR symbol in programming differ from logical AND and logical OR symbols?
The XOR symbol ⊕ is typically represented by ^ in programming (such as C, Java, Python), while logical AND uses &&, and logical OR uses ||. In mathematics and logic, ⊕ or ⊻ is used as the XOR symbol. In programming, ^ is a bitwise operator that operates on binary bits rather than Boolean values.
What are the practical applications of the XOR symbol?
The XOR symbol has very wide applications: ① in cryptography for stream ciphers (plaintext ⊕ key = ciphertext); ② data verification (RAID5 uses XOR to calculate parity); ③ graphics processing (XOR drawing enables eraser effects); ④ algorithm problems like finding the unique number that appears only once, etc.
Why is XOR also called a "half adder"?
Because in binary arithmetic, the XOR result exactly equals addition without considering the carry: 0⊕0=0, 0⊕1=1, 1⊕0=1, 1⊕1=0. This is precisely the "sum" output of a half adder, while the carry output is produced by an AND operation. Thus the ⊕ XOR symbol is a core component of digital circuit adders.
How to type the XOR symbol on a mobile phone?
On iOS, switch to the symbol keyboard and find ⊕ in the mathematical symbols section; on Android, it is usually included in the math section of the symbol panel. Both systems allow typing xor and selecting ⊕ from the candidates. The easiest way is still to simply copy and paste ⊕.