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Negadecimal

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

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Negadecimal -

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

dCode retains ownership of the "Negadecimal" source code. Except explicit open source licence (indicated Creative Commons / free), the "Negadecimal" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Negadecimal" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Negadecimal" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
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Negadecimal on dCode.fr [online website], retrieved on 2024-06-14, https://www.dcode.fr/negadecimal-base

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