To be or not to be, that is the question.

—Shakespeare on Boolean algebra

This chapter discusses bit-oriented operations. A bit is the smallest unit of information; normally represented by the values 1 and 0. (Other representations include on/off, true/false, and yes/no.) Bit manipulations are used to control the machine at the lowest level. They allow the programmer to get "under the hood" of the machine. Many higher-level programs will never need bit operations. Low-level coding such as writing device drivers or pixel-level graphic programming requires bit operations.

Eight bits together form a byte, represented by the C++
data type **char**. A byte might contain
the following bits: 01100100`.`

The binary number 01100100 can also be written as the hexadecimal number 0x64. (C++ uses the prefix "0x" to indicate a hexadecimal—base 16—number.) Hexadecimal is convenient for representing binary data because each hexadecimal digit represents 4 binary bits. Table 11-1 gives the hexadecimal (hex) to binary conversion.

Thus, the hexadecimal number 0xAF represents the binary number 10101111.

Table 11-1. Hex and binary

Hex | Binary | Hex | Binary |
---|---|---|---|

0 | 0000 | 8 | 1000 |

1 | 0001 | 9 | 1001 |

2 | 0010 | A | 1010 |

3 | 0011 | B | 1011 |

4 | 0100 | C | 1100 |

5 | 0101 | D | 1101 |

6 | 0110 | E | 1110 |

7 | 0111 | F | 1111 |

*Bit,* or *bitwise, operators* allow the programmer to work on individual bits. For example, a short integer holds 16 bits (on most machines). The bit operators treat each of these as an independent bit. By contrast, an add operator treats the 16 bits ...

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