Appendix B Number Systems 1285 (How to cite a web site) The octal
Appendix B Number Systems 1285 The octal number system (base 
and the hexadecimal number system (base 16) are popular primarily because they make it convenient to abbreviate binary numbers. The digits of the octal number system range from 0 to 7. The hexadecimal number system poses a problem because it requires sixteen digits a lowest digit of 0 and a highest digit with a value equivalent to decimal 15 (one less than the base of 16). By convention, we use the letters A through F to represent the hexadecimal digits corresponding to decimal values 10 through 15. Each number system uses positional notation each position in which a digit is written has a different positional value. A particularly important relationship that both the octal number system and the hexadecimal number system have to the binary system is that the bases of octal and hexadecimal (8 and 16 respectively) are powers of the base of the binary number system (base 2). To convert an octal number to a binary number, simply replace each octal digit with its three-digit binary equivalent. To convert a hexadecimal number to a binary number, simply replace each hexadecimal digit with its four-digit binary equivalent. Because we are accustomed to working in decimal, it is convenient to convert a binary, octal or hexadecimal number to decimal to get a sense of the number s real worth. To convert a number to decimal from another base, multiply the decimal equivalent of each digit by its positional value, and sum these products. Computers represent negative numbers using two s complement notation. To form the negative of a value in binary, first form its one s complement by applying Visual Basic s Xoroperator. This reverses the bits of the value. To form the two s complement of a value, simply add one to the value s one s complement. TERMINOLOGY base digit base 2 number system hexadecimal number system base 8 number system negative value base 10 number system octal number system base 16 number system one s complement notation binary number system positional notation bitwise complement operator (~) positional value conversions symbol value decimal number system two s complement notation SELF-REVIEW EXERCISES B.1 The bases of the decimal, binary, octal, and hexadecimal number systems are , , , and respectively. B.2 In general, the decimal, octal, and hexadecimal representations of a given binary number contain (more/fewer) digits than the binary number contains. B.3 (True/False) A popular reason for using the decimal number system is that it forms a convenient notation for abbreviating binary numbers simply by substituting one decimal digit per group of four binary bits. B.4 The (octal / hexadecimal / decimal) representation of a large binary value is the most concise (of the given alternatives).
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