Chapter 11. Bit Operations

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