Tool to convert and calculate numbers in base -10, also called negadecimal base (positional numeral system in base minus ten)
Negadecimal - dCode
Tag(s) : Arithmetics
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Negadecimal
Negadecimal to Decimal Converter
Decimal to Negadecimal Converter
Answers to Questions (FAQ)
What is Negadecimal? (Definition)
The negadecimal system is the name given to the positional numeral system in base $ -10 $ (negative/minus ten radix).
For every number $ N $ written in radix $ -10 $ and made of digits $ a_n, a_{n-1}, \cdots, a_1, a_0 $ then $$ N = \sum_{i=0} a_i \times (-10)^i $$ or the following calculation: $ N = a_n(-10)^n + \cdots + a_1(-10)^1 + a_0(-10)^0 $
How to convert a number into negadecimal?
To change the base from a decimal number (base 10) to negadecimal (base -10), apply the algorithm:
N = []
While (n != 0) {
r = n % (-10)
n = floor( n / (-10) )
if (r < 0) {
n += 1
r += 10
}
N = [r,N]
}
Example: $ 123_{(10)} $ go througn the steps: $ r = 123 % (-10) = -7 $, $ n = \lfloor 123/(-10) \rfloor = -13 $ as $ r < 0 $, $ n = -12 $ and $ r = -7 + 10 = 3 $ so the last digit is $ 3 $. Continue to get $ 823_{(-10)} $
How to convert a negadecimal number into decimal?
To calculate the decimal value of a number in radix -10, apply the formula: $$ N = \sum_{i=0} a_i \times (-10)^i $$ with $ a_i $ the digits of $ N $.
Example: $ 789_{(-10)} = 7 \times (-10)^2 + 8 \times (-10)^1 + 9 \times (-10)^0 = 7 \times 100 + 8 \times (-10) + 9 = 629_{(10)} $
Why using negadecimal?
Negadecimal has the advantage of being able to store negative numbers without a minus - sign.
Source code
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