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Tool to convert and calculate numbers in base -10, also called negadecimal base (positional numeral system in base minus ten)

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Tag(s) : Arithmetics

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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: $789_{(-10)} = 7 \times (-10)^2 + 8 \times (-10)^1 + 9 \times (-10)^0 = 7 \times 100 + 8 \times (-10) + 9 = 629_{(10)}$

Negadecimal has the advantage of being able to store negative numbers without a minus - sign.

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