Section 4.3: Different Numeration Systems

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4.3 Outline

  1. Computer numeration systems
    1. binary (base 2)
    2. octal (base 8)
    3. hexadecimal (base 16)
  2. Number of symbols
    1. grouping in various bases
    2. base b
  3. Change from base b to base 10
  4. Change from base 10 to base b

4.3 Essential Ideas

Don’t be intimidated by the “base b” discussion. The variable b refers to any particular base (a counting number). Study Table 4.7, and note that the number symbols is the same as the base. The process of changing from some base to base 10 is to write the number in expanded notation and then use the order of operations to simplify the arithmetic. The change from base 10 to another base b is done by repeated division by the b.