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base (number)
The number upon which a number system is based; this is also the number of different characters or figures needed by the number system. The base, or radix, of our familiar decimal system is 10. Thus, there are ten symbols, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, and a decimal number is written right to left in terms of units, tens, hundreds, and so on. Each move to the left represents a jump by a power of 10. The decimal number 375, for example, equals (3 × 102) + (7 × 10) + (5 × 1). This can easily be written to another base. Decimal 37510 becomes in octal (base 8) 5678 = (5 × 82) + (6 × 8) + (7 × 1), or in binary (base 2) 1011110012 = (1 × 28) + (0 × 27) + (1 × 26) + (1 × 25) + (1 × 24) + (1 × 23) + (0 × 22) + (0 × 2) + (1 × 1).
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• MATHEMATICS
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