ASCII Characters
Characters and text map characters onto binary numbers in a standard way. The ASCII (American Standard Code for Information Interchange) standard uses 8-bit numbers for each character. Therefore, a total of 256 characters can be represented, although usually only 128 are commonly used. Unicode uses 16-bit numbers for each character, for a total of 216 = 65536 characters. Unicode characters are used in the Java programming languages and HTML (Hypertext Markup Language). Both the ASCII and Unicode representations are discussed in more detail in the next section.
Although the decimal and binary number systems are the most commonly used – the former for the regular representation of numbers and the latter for digital computer systems – other number are also used, some of which are useful in computing. The octal system is the base-8 system, with digits 0, 1, 2, 3, 4, 5, 6, and 7. Conversion from binary to octal is straightforward. The binary number is separated into groups of 3 bits to represent an octal digit, as 8 = 23. For example, 1011 11002 is represented in octal by through groups of three bits:
1011 11002 = 010 111 1002 = 2748. Note that a leading “0” needed to be added appended to the left of the binary number so that three groups of three bits result. To verify the result, powers of 8 are used:
1011 11002 = (1 x 27) + (0 x 26) + (1 x 25) + (1 x 24) + (1 x 23) + (1 x 22) + (0 x 21) + (0 x 20) = 128 + 0 + 32 + 16 + 8 + 4 + 0 + 0 = 18810
2748 = (2 x 82) + (7 x 81) + (4 x 80) = (2 x 64) + (7 ´ 8) + (4 ´ 1) = 128 + 56 + 4 = 18810.