Bit shifting
26 Sep 2021We have two main bit shifting operators:
>>right shift<<left shift
Left Shift («)
Essentially moves the bits N to the left.
For instance, let’s say I have the number 6. This can represented by the following binary (representing a byte)
00000110
If we were to shift this number by 1, we would get the following:
6 # 00000110
6 << 1 # 00001100
Shifting left is actually equivalent to multiplying by powers of two so:
6 << 1 == 6 * 2^1 == 6 * 2 == 12
6 << 2 == 6 * 2^2 == 6 * 4 == 24
6 << 3 == 6 * 2^3 == 6 * 8 == 48
Right Shift (»)
Opposite of the left shift, moves the bits to the right. Let’s look at the 6 example again!
6 # 00000110
6 >> 1 # 00000011 (3)
6 >> 2 # 00000001 (1)
6 >> 3 # 00000000 (0)
Shifting right is actually equivalent to dividing by powers of two and rounding down:
6 >> 1 == 6 / 2^1 == 6 / 2 == 3
6 >> 2 == 6 / 2^2 == 6 / 4 == 1 (1.5 rounded down)
6 >> 3 == 6 / 2^3 == 6 / 8 == 0 (0.75 rounded down)
Application
Bit shifting can be used to extract certain specific values from a ‘bitfield’, where data is encoded at the bit level for a value.
For instance, in 8-bit color, we have 3 colors that we can assign to the 8 bits (1 byte). We could assign the 1 byte to the colors like this:
Bit 7 6 5 4 3 2 1 0
Data R R R G G G B B
This gives us 4 possible blue values, 8 possible green values and 8 possible red values.
Let’s say we want to extract the green value, we first need to create a mask. The mask will remove all the data we don’t want.
Data R R R G G G B B
Color 1 1 0 1 0 1 1 1 (215)
Green Mask 0 0 0 1 1 1 0 0 (28)
masked = color & greenMask (& ensures only bits of 1 is kept)
masked 0 0 0 1 0 1 0 0 (20)
We then just need to get the correct value by shifting the bits
Data R R R G G G B B
masked 0 0 0 1 0 1 0 0 (20)
greenValue = masked >> 2 = 5
And there we have it, we have decoded that our color byte has the green value of ‘5’.
Sources
https://stackoverflow.com/questions/141525/what-are-bitwise-shift-bit-shift-operators-and-how-do-they-work