Bitwise Operators

Unlike many other languages, C/C++ supports a full complement of bitwise
operators. Since C was designed to take the place of assembly language for most
programming tasks, it needed to be able to support many operations that can be done
in assembler, including operations on bits. Bitwise operation refers to testing, setting, or
shifting the actual bits in a byte or word, which correspond to the char and int data
types and variants. You cannot use bitwise operations on float, double, long double,
void, bool, or other, more complex types. Table 2-6 lists the operators that apply to
bitwise operations. These operations are applied to the individual bits of the
operands.

Operator          Action
&                      AND
|                        OR
^                Exclusive OR (XOR)
~                 One's complement (NOT)

>>                  Shift right
<<                    Shift left

Table 2-6. Bitwise Operators

The bitwise AND, OR, and NOT (one's complement) are governed by the same
truth table as their logical equivalents, except that they work bit by bit. The exclusive
OR has the truth table shown here:
p   q    p^q
0   0     0
1   0     1
1   1     0
0   1     1
As the table indicates, the outcome of an XOR is true only if exactly one of the
operands is true; otherwise, it is false.
Bitwise operations most often find application in device drivers—such as modem
programs, disk file routines, and printer routines —because the bitwise operations
can be used to mask off certain bits, such as parity. (The parity bit confirms that the
rest of the bits in the byte are unchanged. It is usually the high-order bit in each byte.)
Think of the bitwise AND as a way to clear a bit. That is, any bit that is 0 in either
operand causes the corresponding bit in the outcome to be set to 0. For example, the
following function reads a character from the modem port and resets the parity bit to 0:
char get_char_from_modem(void)
{
char ch;
ch = read_modem(); /* get a character from the
modem port */
return(ch & 127);
}

Parity is often indicated by the eighth bit, which is set to 0 by ANDing it with a
byte that has bits 1 through 7 set to 1 and bit 8 set to 0. The expression ch & 127 means
to AND together the bits in ch with the bits that make up the number 127. The net
result is that the eighth bit of ch is set to 0. In the following example, assume that ch
had received the character "A" and had the parity bit set:
The bitwise OR, as the reverse of AND, can be used to set a bit. Any bit that is set
to 1 in either operand causes the corresponding bit in the outcome to be set to 1. For
example, the following is 128 | 3:
Ill 2-2
An exclusive OR, usually abbreviated XOR, will set a bit on if and only if the bits
being compared are different. For example, 127 ^120 is
Remember, relational and logical operators always produce a result that is either
true or false, whereas the similar bitwise operations may produce any arbitrary value
in accordance with the specific operation. In other words, bitwise operations may
produce values other than 0 or 1, while logical operators will always evaluate to 0 or 1.
The bit-shift operators, >> and <<, move all bits in a variable to the right or left as
specified. The general form of the shift-right statement is
 

1 0 0 0 0 0 0 0 128 in binary
0 0 0 0 0 0 1 1 3 in binary
¦___________ bitwise OR
1 0 0 0 0 0 1 1 result
0 1 1 1 1 1 1 1 127 in binary
0 1 1 1 1 0 0 0 120 in binary
^___________ bitwise XOR
0 0 0 0 0 1 1 1 result
Parity bit
1 1 0 0 0 0 0 1 ch containing an "A" with parity set
0 1 1 1 1 1 1 1 127 in binary
&___________ bitwise AND
0 1 0 0 0 0 0 1 "A"without parity

The bitwise OR, as the reverse of AND, can be used to set a bit. Any bit that is set
to 1 in either operand causes the corresponding bit in the outcome to be set to 1. For
example, the following is 128 | 3:
Ill 2-2
An exclusive OR, usually abbreviated XOR, will set a bit on if and only if the bits
being compared are different. For example, 127 ^120 is
Remember, relational and logical operators always produce a result that is either
true or false, whereas the similar bitwise operations may produce any arbitrary value
in accordance with the specific operation. In other words, bitwise operations may
produce values other than 0 or 1, while logical operators will always evaluate to 0 or 1.
The bit-shift operators, >> and <<, move all bits in a variable to the right or left as
specified. The general form of the shift-right statement isvariable >> number of bit positions
The general form of the shift-left statement is
variable << number of bit positions
As bits are shifted off one end, 0's are brought in the other end. (In the case of a
signed, negative integer, a right shift will cause a 1 to be brought in so that the sign bit
is preserved.) Remember, a shift is not a rotate. That is, the bits shifted off one end do
not come back around to the other. The bits shifted off are lost.
Bit-shift operations can be very useful when you are decoding input from an
external device, like a D/A converter, and reading status information. The bitwise shift
operators can also quickly multiply and divide integers. A shift right effectively divides
a number by 2 and a shift left multiplies it by 2, as shown in Table 2-7. The following
program illustrates the shift operators:
/* A bit shift example. */
#include <stdio.h>
int main(void)
{
unsigned int i;
int j;
i = 1;
/* left shifts */
for(j=0; j<4; j++) {
i = i << 1; /* left shift i by 1, which
is same as a multiply by 2 */
printf("Left shift %d: %d\n", j, i);
}
/* right shifts */
for(j=0; j<4; j++) {
i = i >> 1; /* right shift i by 1, which
is same as a division by 2 */
printf("Right shift %d: %d\n", j, i);
}
return 0;
}

unsigned char x;                     x as each statement executes                 value of x
x = 7;                                                   0 0 0 0 0 1 1 1                           7
x = x<<1;                                            0 0 0 0 1 1 1 0                           14
x = x<<3;                                            0 1 1 1 0 0 0 0                          112
x = x<<2;                                           1 1 0 0 0 0 0 0                           192
x = x>>1;                                            0 1 1 0 0 0 0 0                            96
x = x>>2;                                             0 0 0 1 1 0 0 0                           24

*Each left shift multiplies by 2. Notice that information has been lost after x<<2 because
a bit was shifted off the end.
**Each right shift divides by 2. Notice that subsequent divisions do not bring back any
lost bits.
Table 2-7. Multiplication and Division with Shift Operators

The one's complement operator, ~, reverses the state of each bit in its operand. That
is, all 1's are set to 0, and all 0's are set to 1.
The bitwise operators are often used in cipher routines. If you want to make a disk
file appear unreadable, perform some bitwise manipulations on it. One of the simplest
methods is to complement each byte by using the one's complement to reverse each bit
in the byte, as is shown here:
Notice that a sequence of two complements in a row always produces the original
number. Thus, the first complement represents the coded version of that byte. The
second complement decodes the byte to its original value.
You could use the encode() function shown here to encode a character.
/* A simple cipher function. */
char encode(char ch)
{return(~ch); /* complement it */
}
Of course, a file encoded using encode() would be very easy to crack!