Bitwise Operators
& AND
| OR
^ XOR
~ NOT
Truth Tables
AND (“&”)
truth table
+--------+--------+-----------------+ | bit a | bit b | a & b (a AND b) | +--------+--------+-----------------+ | 0 | 0 | 0 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 1 | +--------+--------+-----------------+
byte example
11001000
& 10111000
--------
= 10001000
OR (“|”)
truth table
+--------+--------+----------------+ | bit a | bit b | a | b (a OR b) | +--------+--------+----------------+ | 0 | 0 | 0 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 1 | +--------+--------+----------------+
byte example
11001000
| 10111000
--------
= 11111000
XOR (“^”)
truth table
+--------+--------+-----------------+ | bit a | bit b | a ^ b (a XOR b) | +--------+--------+-----------------+ | 0 | 0 | 0 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 0 | +--------+--------+-----------------+
byte example
11001000
^ 10111000
--------
= 01110000
NOT (“~”)
truth table
+--------+----------------------+ | bit a | ~a (complement of a) | +--------+----------------------+ | 0 | 1 | | 1 | 0 | +--------+----------------------+
byte example
~ 11001000
--------
= 00110111
Shift Operators
>> right shift (8 bits variable)
0x80>>0 = 0b10000000 0x80>>1 = 0b01000000 0x80>>2 = 0b00100000 0x80>>3 = 0b00010000 0x80>>4 = 0b00001000 0x80>>5 = 0b00000100 0x80>>6 = 0b00000010 0x80>>7 = 0b00000001
<< left shift (8 bits variable)
0x01<<0 = 0b00000001 0x01<<1 = 0b00000010 0x01<<2 = 0b00000100 0x01<<3 = 0b00001000 0x01<<4 = 0b00010000 0x01<<5 = 0b00100000 0x01<<6 = 0b01000000 0x01<<7 = 0b10000000
Examples
# Set a bit BYTE |= (1 << i); # Clear a bit BYTE &= ~(1 << i); # Toggle a bit BYTE ^= (1 << i); # Set bits i and k BYTE ^= ((1 << i) | (1 << k));
Macros
#define BV(bit) (1 << (bit)) #define setBit(byte, bit) (byte |= BV(bit)) #define clearBit(byte, bit) (byte &= ~BV(bit)) #define toggleBit(byte, bit) (byte ^= BV(bit))
