“base(for representation of numbers)”的概念、定义、翻译、参考文献-科学参考

base(for representation of numbers)

Mathematics

The integer represented as 4703 in standard decimal notation is written in this way because

$4703 = (4 \times 10^{3}) + (7 \times 10^{2}) + (0 \times 10) + 3 .$

The same integer can be written in terms of powers of 8 as follows:

$4703 = (1 \times 8^{4}) + (1 \times 8^{3}) + (1 \times 8^{2}) + (3 \times 8) + 7.$

The expression on the right-hand side is abbreviated to 11137₈ and is the representation of this number to base 8 (or octal). In general, if g is an integer greater than 1, any positive integer a can be written uniquely as

$a = c_{n} g^{n} + c_{n - 1} g^{n - 1} + \dots + c_{1} g + c_{0},$

where each c_i is a non-negative integer less than g. This is the representation of a to base g and is abbreviated to ${c_{n} c_{n - 1} \dots c_{1} c_{0}}_{g}$ . Real numbers, not just integers, can also be written to any base, by using figures after a ‘decimal’ point, just as familiar decimal representations of real numbers are written to base 10. See also binary representation, decimal, hexadecimal.

单词	base(for representation of numbers)
释义	base(for representation of numbers) Mathematics The integer represented as 4703 in standard decimal notation is written in this way because $4703 = (4 \times 10^{3}) + (7 \times 10^{2}) + (0 \times 10) + 3 .$ The same integer can be written in terms of powers of 8 as follows: $4703 = (1 \times 8^{4}) + (1 \times 8^{3}) + (1 \times 8^{2}) + (3 \times 8) + 7.$ The expression on the right-hand side is abbreviated to 11137₈ and is the representation of this number to base 8 (or octal). In general, if g is an integer greater than 1, any positive integer a can be written uniquely as $a = c_{n} g^{n} + c_{n - 1} g^{n - 1} + \dots + c_{1} g + c_{0},$ where each c_i is a non-negative integer less than g. This is the representation of a to base g and is abbreviated to ${c_{n} c_{n - 1} \dots c_{1} c_{0}}_{g}$ . Real numbers, not just integers, can also be written to any base, by using figures after a ‘decimal’ point, just as familiar decimal representations of real numbers are written to base 10. See also binary representation, decimal, hexadecimal.
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