Bitwise Operators: Difference between revisions

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A few properties of AND that aren't readily apparent. These assume an 8-bit architecture but also apply to other architectures as well if you add enough trailing ones to fill the variable size. (8 bit was chosen for brevity's sake.)

A few properties of <code>AND</code> that aren't readily apparent. These assume an 8-bit architecture but also apply to other architectures as well if you add enough trailing ones to fill the variable size. (8 bit was chosen for brevity's sake.)

For all numbers A:

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===Random Chance===

Given the output of a random number generator with all equally likely outcomes, you can use AND with that output to create random occurrences. If <math>n</math> is a power of 2, then to create a random event with probability <math>1/n</math>, you just need to AND the RNG output with <math>n-1</math>. In the example below, <code>rand</code> is a randomly generated 8-bit value.

Given the output of a random number generator with all equally likely outcomes, you can use AND with that output to create random occurrences. If <math>n</math> is a power of 2, then to create a random event with probability <math>1/n</math>, you just need to <code>AND</code> the RNG output with <math>n-1</math>. In the example below, <code>rand</code> is a randomly generated 8-bit value.

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==OR==

Bitwise OR, often abbreviated to <code>|</code> (SHIFT+\), compares each individual bit of two different numbers, and outputs a 0 if both are 0, and a 1 otherwise.

Bitwise <code>OR</code>, often abbreviated to <code>|</code> (SHIFT+\), compares each individual bit of two different numbers, and outputs a 0 if both are 0, and a 1 otherwise.

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==XOR==

eXclusive OR, often abbreviated to <code>^</code> or called <code>EOR</code> in some languages, compares each individual bit of two different numbers, and outputs a 1 if they are different and 0 if they are the same.

eXclusive OR, often abbreviated to <code>XOR</code>, <code>^</code> or called <code>EOR</code> in some languages, compares each individual bit of two different numbers, and outputs a 1 if they are different and 0 if they are the same.

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* If <code>A XOR B = C</code>, then <code>A XOR C = B</code> and <code>B XOR C = A</code>.

* A bit <code>XOR</code>'d with 1 will flip. A bit <code>XOR</code>'d with zero won't change.

* A bitwise <code>NOT</code> is the same as <code>XOR -1</code>.

==NOT==

A bitwise <code>NOT</code>, or <code>~</code> takes one number as an argument and flips all its bits. This has its uses, especially when reading video game controllers, but is a little more limited than the others.

===Toggling===