Unless your instructor explicitly assigns this section, you may skip it for now and return later when these operations are more relevant.
C++ inherits six bitwise operators from C. Bitwise operations are always available in assembly language but are less common in higher-level languages. Including these operators in C made it possible to write operating systems and device drivers in C rather than in assembly. Most bitwise operators require two integer arguments, but complement is a unary operator. Three operators act on the corresponding bits of the two operands; we can conveniently summarize these and the complement operators with truth tables. Two operators treat one operand as a string of bits and shift them to the left or the right. We'll often view one or both the operands as a short string of bits for our convenience and ease of illustration.
The basic bitwise operators are simple enough to describe them with simple truth tables. When we use these operators, it's convenient to think about or view both operands in binary: 1s and 0s. Each 0-value corresponds to false and each 1-value corresponds to true. A simple example follows each truth table, which illustrates the meaning of "the bitwise operators operate on the corresponding bits of the two operands." The result of combining two bits with a bitwise operator is a single bit. The following figures detail
12 & 9 = 8 1100 & 1001 ------ 1000 |
12 | 9 = 13 1100 | 1001 ------ 1101 |
||||||||||||||||||||||||||||||
12 ^ 9 = 5 1100 ^ 1001 ------ 0101 |
~12 = 3 ~ 1100 ------ 0011 |
Viewed in base-10 (below each truth table in the figures above), the bitwise operations don't seem to make much sense. Nevertheless, they are useful in specialized processes, especially when one operand is a constant, often called a bitmask. C++ does not have a notation for representing binary constants, so integer constants are typically denoted in hexadecimal (or occasionally in octal). A single hexadecimal digit corresponds to a nibble (i.e., to 4-bits). So, we can compactly specify each 4-bits of a constant as a single hexadecimal digit.
Decimal | Octal | Hexadecimal | Binary |
---|---|---|---|
0 | 0 | 0x0 | 0000 |
1 | 01 | 0x1 | 0001 |
2 | 02 | 0x2 | 0010 |
3 | 03 | 0x3 | 0011 |
4 | 04 | 0x4 | 0100 |
5 | 05 | 0x5 | 0101 |
6 | 06 | 0x6 | 0110 |
7 | 07 | 0x7 | 0110 |
8 | 010 | 0x8 | 1000 |
9 | 011 | 0x9 | 1001 |
10 | 012 | 0xa | 1010 |
11 | 013 | 0xb | 1011 |
12 | 014 | 0xc | 1100 |
13 | 015 | 0xd | 1101 |
14 | 016 | 0xe | 1110 |
15 | 017 | 0xf | 1111 |
One of the most common uses for bitwise operations is to set, reset, and test bits stored in a multi-bit data structure. A "multi-bit data structure" may be as simple as an integer, which may hold anywhere from 8- to 64-bits, or an array (chapter 7) of integers. Multi-bit data are often called bit fields, bit sets, bit vectors, bit maps, bit strings, etc.
Bit fields are often used to represent a wide variety of settings or conditions compactly. Each bit acts as a switch. A 1 indicates that a setting is on, while a 0 indicates that the setting is off. Programs often use bitwise-OR and bitwise-AND operators in conjunction with constant bit fields, called bitmasks, to switch bits on and off respectively, which corresponds to switching settings on or off.
Input and output operations in a C++ program generally takes place through stream objects (e.g., cin and cout). Programmers control the behaviors of these objects with a set of 1-bit switches or flags. Each bit corresponds to a specific behavior - setting the bit to 0 disables the behavior, and setting it to 1 enables it. Programmers use named bitmasks (i.e., constant values) and bitwise operators to bit settings. Four of the file I/O bitmasks illustrate the concept:
in = 0x01 = 00000000000000000000000000000001
out = 0x02 = 00000000000000000000000000000010
app = 0x08 = 00000000000000000000000000001000
binary = 0x20 = 00000000000000000000000000100000
To create a value that will switch on all four behaviors, a programmer might write an assignment statement such as:
int mode = in | out | app | binary;
The bitwise-OR operations produce the bit field: 00000000000000000000000000101011
, which the programmer could then use to open a file that has the combined behaviors.
The library code that actually opens the file may look similar to the following:
if (mode & binary != 0) { // then configure the file for reading or writing in binary mode } if (mode & app != 0) { // then configure the file for writing in append mode } . . . .
The bitwise-AND operation switches off all of the bits except the one corresponding to the binary bitmask. The magnitude (i.e., the exact value) of mode & binary
is not important; all that is important is that the value is not 0. If "binary" had been left out of the assignment statement above that calculated "mode," then the expression mode & binary
would produce a 0 and the code for configuring the file for binary I/O would be skipped.
The two bit-shift operators should look familiar to you, not because we have used them before, but because they are reused as the output and input operators introduced previously. Both operands are integers, and we will continue to view the left-hand operand in binary but will now view the right-hand operand in decimal. Both bit-shift operators treat the left-hand operand as a string of 1's and 0's that are shifted either left or right by the number of places indicated by the right-hand operand. Shifting may seem confusing but is easy to understand when illustrated with an example.
The left shift operator, <<
moves the bits in an integer to the left. The right-hand operand specifies how many places to shift the bits. For example:
The right shift operator, >>
is similar to the left shift operator but is a little more complicated. The right shift operator moves the bits in the left-hand operand to the right by the number of places specified by the right-hand operand. The bits shifted out on the right side are discarded as expected. But it is how the operation fills the empty spaces on the left that makes the right shift operator complicated.
Without programmer intervention it is the underlying hardware that determines how the spaces vacated by the shift are filled. (The ANSI standard calls such features implementation dependent.) Some hardware implements sign extension (i.e., it fills the empty spaces a copy of the left most bit), and some hardware does not (i.e., it fills the empty spaces with 0's).
Fortunately, programmers can intervene. The highest-order bit in a signed integer, the sign bit, denotes a negative value when it is 1 and a non-negative value when it is 0. A negative value is generally not needed when an integer stores a bit pattern, and so the easy "fix" is to define the integer as unsigned
. (It's quite common to use unsigned integers, variables, and constants with all of the bitwise operators.) When the right shift operator's left operand is unsigned, then the empty spaces on the left are always filled with 0's regardless of how the hardware behaves by default.
The following examples demonstrate the right shift operator with and without sign extension:
Earlier in the chapter, we saw that C++ allows a shorthand notation with arithmetic operators called "Operation With Assignment." The operation with assignment notation may also be used with all the binary bitwise operators as well.
Operation With Assignment | Meaning |
---|---|
V &= E | V = V & E |
V |= E | V = V | E |
V ^= E | V = V ^ E |
V >>= I | V = V >> I |
V <<= I | V = V << I |