First, let's take an example:

10011
01011
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These are the binary representation of two numbers. Now, we go through bit by bit and we take the result by these rules:

if both bits are set (equal to 1) then the result bit is 1

otherwise the result bit is 0

so, the above is this:

10011 #from above
01011 #from above
00011 #result
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There are also the operators OR,XOR,and more. OR is the result bit is 1 if either bit is set, XOR is the result bit is 1 if one but not both of the bits are set.

The 15 year old, freshman programmer,
Stephen Rawls

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