Just taking the first of those problem lines should make it clear to you:

print ((128&$bin)/128);

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This takes your number in $bin and bitwise-ANDs it with 128 (27 = 128). The result of that will be either 128 or 0. Divide that result by 128 and you get zero or one.

Repeat for 64 (26) down to 1 (20) and you have your binary number.

Take 123, for example

123 & 128 = 0 / 128 = 0
123 & 64 = 64 / 64 = 1
123 & 32 = 32 / 32 = 1
123 & 16 = 16 / 16 = 1
123 & 8 = 8 / 8 = 1
123 & 4 = 0 / 4 = 0
123 & 2 = 2 / 2 = 1
123 & 1 = 1 / 1 = 1
Read the binary, top to bottom: 12310 = 011110112

update: added the example

In reply to Re: Bitwise and operator question by FunkyMonk
in thread Bitwise and operator question by Severy

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