How Do Addition and Multiplication Tables Work in Base -5?

[1+1=1]

i am curious as to how this would look. i wonder how the addition tables would look in base -5? would the multiplication look the same?

here is what i know so far:

addition multiplication
0 1 2 3 4 0 0 0 0 0
1 2 3 4 10 0 1 2 3 4
2 3 4 10 11 0 2 4 11 13
3 4 10 11 12 0 3 11 14 22
4 10 11 12 13 0 4 13 22 31

i know this, but where are the negative signs at??

 

[geraldmcgarvey]

Negative bases

Interesting concept, here's some links to info on negative bases:
http://mathforum.org/library/drmath/view/55710.html
http://www.maa.org/devlin/devlinfeb.html
One thing the articles point out is that no sign is necessary,
instead negative and positive numbers differ in their number
of digits.

 

[1+1=1]

these negative bases are quite interesting, although are they reallly used all that much? i know that everyone I've talked to is basically saying "no." however, almost anyone could make up their own number system, but no one else could understand it.

 

[Gokul43201]

In Alice in Wonderland, when Alice has fallen down the rabbit hole, she wonders if she's swapped places with someone called Mabel. To discover her true identity, she recites the 4 times table:

"But if I'm not the same, the next question is, 'Who in the world am I?' Ah, that's the great puzzle!... and I'm sure I can't be Mabel, for I know all sorts of things, and she, oh! she knows such a very little!... I'll try all the things I used to know. Let me see: four times five is twelve, and four times six is thirteen, and four times seven is -- oh dear! I shall never get to twenty at that rate!"

Figure out why this is true !

 

[1+1=1]

this definitely has something to do with numbers that are NOT base 10. other than that, i'll have to sleep on it.

 

[geraldmcgarvey]

Here's a little more on 'negabinary' which was used by
experimental Polish computers in 1950:
http://encyclopedia.thefreedictionary.com/Negabinary
http://mathworld.wolfram.com/Negabinary.html
also negadecimal:
http://mathworld.wolfram.com/Negadecimal.html
It looks like negative bases are not used, perhaps
because working with them is unnecessarily complicated.