“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
随便看	Scheiner, Christoph (1573–1650) Scheinwoodian Scheler, Max Ferdinand (1874–1928) Schelling, Friedrich Wilhelm Joseph von (1775–1854) schema schematic schematic flow diagram SCHEME Schengen Area Schering bridge Scheuchzer, Johann Jacob (1672–1733) Schiaparelli Schiaparelli, Giovanni Virginio Schiaparelli, Giovanni Virginio (1835–1910) schiefspiegler telescope Schiff base Schiff, Moritz Schiff’s base (DRAFT) Schiff’s reagent schiller Schiller, Ferdinand Canning Scott (1864–1937) Schiller, Johann Cristoph Friedrich (1759–1805) Schimper, Andreas Franz Wilhelm Schindewolf, Otto H. (1896–1971) Schirach, Baldur von (1907–74)