“number system”的概念、定义、翻译、参考文献-科学参考

number system

Computer

Although early number systems were not positional, all of the number systems most commonly used today are positional systems: the value of a number in such a system is determined not just by the digits in the number but also by the position in the number of each of the digits. If a positional system has a fixed radix (or fixed base) R then each digit a_i in any number
$a_{n} a_{n - 1} \dots a_{0}$
is an integer in the range 0 to (R – 1) and the number is interpreted as
$a_{n} R^{n} + a_{n - 1} R^{n - 1} + \dots + a_{1} R^{1} + a_{0} R^{0}$
Since this is a polynomial in R, such numbers are sometimes called polynomial numbers. The decimal and binary systems are both fixed-radix systems, with a radix of 10 and 2, respectively.
Fractional values can also be represented in a fixed-radix system. Thus,
$0 \cdot a_{1} a_{2} \dots a_{n}$
is interpreted as
$a_{1} R^{- 1} + a_{2} R^{- 2} + \dots + a_{n} R^{- n}$
In a mixed-radix (or mixed-base) system, the digit a_i in any number
$a_{n} a_{n - 1} \dots a_{0}$
lies in the range 0 to R_i, where R_i is not the same for every i. The number is then interpreted as
$(\dots ((a_{n} R_{n - 1}) + a_{n - 1}) R_{n - 2} + \dots + a_{1}) R_{0} + a_{0}$
for example, 122 days 17 hours 35 minutes 22 seconds is equal to
$(((((1 \times 10) + 2) 10 + 2) 24 + 17) 60 + 35) 60 + 22$
seconds

单词	number system
释义	number system Computer Although early number systems were not positional, all of the number systems most commonly used today are positional systems: the value of a number in such a system is determined not just by the digits in the number but also by the position in the number of each of the digits. If a positional system has a fixed radix (or fixed base) R then each digit a_i in any number $a_{n} a_{n - 1} \dots a_{0}$ is an integer in the range 0 to (R – 1) and the number is interpreted as $a_{n} R^{n} + a_{n - 1} R^{n - 1} + \dots + a_{1} R^{1} + a_{0} R^{0}$ Since this is a polynomial in R, such numbers are sometimes called polynomial numbers. The decimal and binary systems are both fixed-radix systems, with a radix of 10 and 2, respectively. Fractional values can also be represented in a fixed-radix system. Thus, $0 \cdot a_{1} a_{2} \dots a_{n}$ is interpreted as $a_{1} R^{- 1} + a_{2} R^{- 2} + \dots + a_{n} R^{- n}$ In a mixed-radix (or mixed-base) system, the digit a_i in any number $a_{n} a_{n - 1} \dots a_{0}$ lies in the range 0 to R_i, where R_i is not the same for every i. The number is then interpreted as $(\dots ((a_{n} R_{n - 1}) + a_{n - 1}) R_{n - 2} + \dots + a_{1}) R_{0} + a_{0}$ for example, 122 days 17 hours 35 minutes 22 seconds is equal to $(((((1 \times 10) + 2) 10 + 2) 24 + 17) 60 + 35) 60 + 22$ seconds
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