Bitwise Operators

$a & $b     And         Bits that are set in both $a and $b are set.
$a | $b     Or          Bits that are set in either $a or $b are set.
$a ^ $b     Xor         Bits that are set in $a or $b but not both are set.
~ $a        Not         Bits that are set in $a are not set, and vice versa.
$a << $b    Shift left  Shift the bits of $a $b steps to the left (each step means "multiply by two")
$a >> $b    Shift right Shift the bits of $a $b steps to the right (each step means "divide by two")

& (bitwise logical and)

If both binary numbers have a 1 in the same place, it's a 1. If one place has a 1 and one place has a 0, in & you keep the 0.

17 & 6 = 0
# 00010001 17
# 00000110 6
# 00000000 0

| (bitwise logical or)

If both binary numbers have a 1 in the same place, it's a 1. If one place has a 1 and one place has a 0, in | you keep the 1.

17 | 6 = 23
# 00010001 17
# 00000110 6
# 00010111 23

^ (bitwise logical exclusive or)

If both binary numbers have the same value in the same place, whether 1 or 0, it's a 0. If they differ, in ^ it is then 1.

17 ^ 23 = 6
# 00010001 17
# 00010111 23
# 00000110 6

<<

17 << 1 = 34 (1 step; each _step_ means multiply by _2_ (it's not 17 * 1, it's 17 * 2))
17 << 2 = 68 (2 steps; each _step_ means multiply by 2; 17 * 2 * 2)