How can I use MathJax / $\TeX$ to format bitwise operations?

Question

There are many symbols available in MathJax / $\TeX$.

How can I format the common bitwise operations using the formatting available on this site?

Answer 1

There are no direct choices for bitwise operators. We have however a few options in this regard, taken from the logical set of operators:

XOR (exclusive OR):

• the symbol $\oplus$ can be created using \oplus
• the symbol $\otimes$ can be created using \otimes

NEG (negation):

• the symbol $\sim$ can be created using \sim
• the symbol $\neg$ can be created using \neg

AND (bitwise AND):

• the symbol $\land$ can be created using \land (logical-AND) or \wedge (but note that ^ is often used to mean XOR in programming languages)
• the symbol $\&$ can be created using \&

OR (bitwise OR):

• the symbol $\lor$ can be created using \lor (logical-OR) or \vee
• the symbol $\circ$ can be created using \circ
• the symbol $|$ can simply be created using a single pipe character |
• the symbol $\parallel$ can be created using \parallel

The shift and round functions can also be formatted:

• $\ll$ means left-shift and can be created using \ll
• $\lll$ means left-rotation and can be created using \lll
• $\gg$ means right-shift and can be created using \gg
• $\ggg$ means right-rotation and can be created using \ggg

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To display these symbols put them in formulas between one \$ sign (inline formula) or two \$\$ signs (centered formula on a separate line). So $a \oplus b$ displays as $a \oplus b$ while $$a \oplus b$$ displays as: $$a \oplus b$$

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Of these the $\oplus\space\&\space\circ$ are probably the ones least reused. Sometimes $+$ (just +) and $\cdot$ (\cdot) are also used in functions to mean OR and AND respectively.

Alternatively it is possible to use $\operatorname{or}$ directly by using \operatorname{or}, which simply displays the text as if it was a function identifier. This will arguably introduce the least confusion.

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This answer just shows how to format bitwise operators. It doesn't show any reason to choose one over the other (unless confusion can arise), it's just used to display the various formatting options.

As you can see, there are many options to choose from. Please make sure we understand the meaning of each operator that you use. 🦉