Bitwise operations

A single byte often carries several pieces of information, like flags in individual bits, or two small numbers in its two halves. To take it apart you need bitwise operations:

• a & b (AND) gives a 1 bit only where both numbers have a 1.
• a | b (OR) gives a 1 bit where either number has a 1.
• a ^ b (XOR) gives a 1 bit where the two bits differ.
• The shift a << n moves the bits n places to the left, which multiplies the number by 2 to the power of n.
• The shift a >> n moves them to the right, which divides the number and drops the fraction.
• ~a flips every bit.

A bitmask is a number you use to pick out the bits you want. The mask 0x0f, which is 0000 1111, isolates the low half of a byte, and the shift >> 4 brings the high half down into its place:

  1010 0110      flags = 0xA6
& 0000 1111      mask  = 0x0f
= 0000 0110      low   = 6

  1010 0110 >> 4 = 0000 1010      high = 10

To find out whether bit n is set, isolate it with its mask and compare the result with zero. Bits are numbered from the right, starting at zero. To flip a single bit, XOR it with its mask. And note that ~ in Python gives a negative number, so mask the result with 0xff to stay within a byte:

(flags & (1 << n)) != 0    # is bit n set?
flags ^ (1 << n)            # flips bit n
~flags & 0xff               # flips every bit