bitwise operations operate one bit at a time

The results can be surprising when you write them in base 10: 8 & 3 = 0

but in binary it makes more sense:

00001000 (8)
& 00000011 (3)
= 00000000

&

Bitwise and: the result is 1 if BOTH bits are 1

1 & 1 = 1
1 & 0 = 0
0 & 0 = 0
11 & 10 = 10

|

Bitwise or: the result is 1 if EITHER bit is a 1

1 | 1 = 1
1 | 0 = 1
0 | 0 = 0
11 | 10 = 11

^

Bitwise xor: the result is 1 if EXACTLY ONE bit is a 1

1 ^ 1 = 0
1 ^ 0 = 1
0 ^ 0 = 0
11 ^ 10 = 01

~

Bitwise not: FLIP all the bits

~0 = 1
~1 = 0
~10 = 01

<<

Left shift: add 0s to the end

1110 <<< 3 = 1110000

<< n is the same as multiplying by 2^n

>>

Right shift: chop bits off the end 01100001 >> 2 = 00011000

>> n is the same as dividing by 2^n

there are actually two right shifts

unsigned right shift

253 >> 1 = 126
11111101 -> 01111110

always pad on the left with a 0

signed right shift

-3 >> 1 = 2
11111101 -> 11111110

if the number is negative, pad on the left with 1 instead of a 0

In some languages, unsigned right shift is >>>. In other languages, both right shifts are >> and the integer’s type determines which is used.