1-3Each of the number systems you will study is built around the following components: the UNIT,NUMBER, and BASE (RADIX).Unit and NumberThe terms unit and number when used with the decimal system are almost self-explanatory. Bydefinition the unit is a single object; that is, an apple, a dollar, a day. A number is a symbol representing aunit or a quantity. The figures 0, 1, 2, and 3 through 9 are the symbols used in the decimal system. Thesesymbols are called Arabic numerals or figures. Other symbols may be used for different number systems.For example, the symbols used with the Roman numeral system are lettersV is the symbol for 5, X for10, M for 1,000, and so forth. We will use Arabic numerals and letters in the number system discussionsin this chapter.Base (Radix)The base, or radix, of a number system tells you the number of symbols used in that system. Thebase of any system is always expressed in decimal numbers. The base, or radix, of the decimal system is10. This means there are 10 symbols0, 1, 2, 3, 4, 5, 6, 7, 8, and 9used in the system. A numbersystem using three symbols0, 1, and 2would be base 3; four symbols would be base 4; and soforth. Remember to count the zero or the symbol used for zero when determining the number of symbolsused in a number system.The base of a number system is indicated by a subscript (decimal number) following the value of thenumber. The following are examples of numerical values in different bases with the subscript to indicatethe base:7592_{10 } 214_{5 }123_{4 }656_{7}You should notice the highest value symbol used in a number system is always one less than the baseof the system. In base 10 the largest value symbol possible is 9; in base 5 it is 4; in base 3 it is 2.Positional Notation and ZeroYou must observe two principles when counting or writing quantities or numerical values. They arethe POSITIONAL NOTATION and the ZERO principles.Positional notation is a system where the value of a number is defined not only by the symbol but bythe symbol’s position. Let’s examine the decimal (base 10) value of 427.5. You know from experience thatthis value is four hundred twenty-seven and one-half. Now examine the position of each number:If 427.5 is the quantity you wish to express, then each number must be in the position shown. If youexchange the positions of the 2 and the 7, then you change the value.

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