Adding in a number system that is Base 5

[chiwawa626]

I dont understand how adding works out when using a diffrent number system.
Lets say we have a base 5 number system, and the digits are in order {0,1,2,3,4}. The numbers i want to add are lets say 1320+4321...how would i go about doing that by hand, without converting to base 10 or any other number system. I dont understand how when you add numbers you would carry things over?

so:

1320
+4321
-------
=?

 

[Sahakiel]

Originally posted by: chiwawa626
I dont understand how adding works out when using a diffrent number system.
Lets say we have a base 5 number system, and the digits are in order {0,1,2,3,4}. The numbers i want to add are lets say 1320+4321...how would i go about doing that by hand, without converting to base 10 or any other number system. I dont understand how when you add numbers you would carry things over?

add it up like you normally do, just carry over after 4?

so:

1320
+4321
-------
=?

11141

 

[DaveSimmons]

Just like in base 10, 3 + 3 = 6 = 1 plus 5 so you carry the 5.

2323
2414

3 + 4 = 7 = 2 + (5 carried left as a 1)
(carry) + 2 + 1 = 4, nothing to carry left
(no carry) + 3 + 4 = 7 = 2 + (5 carried as 1)
(carry) + 2 + 2 = 5 = 0 + (5 carried left)

so the result is
10242

 

[jwells777]

Honestly, it is probably easier to convert to base 10, add, then convert back to the other base if you need to. And the answer to your sample question is 11141 (base 5) or 796 (base 10). If you really want to add in a given number system, you need to understand the modulo function. And as a final point, I am not familiar with any important application of any number system other than base 10 and base 2 (Hex and Octal are just convenient representation used for a fundamentally binary application)

 

[Hector13]

Originally posted by: jwells777
Honestly, it is probably easier to convert to base 10, add, then convert back to the other base if you need to. And the answer to your sample question is 11141 (base 5) or 796 (base 10). If you really want to add in a given number system, you need to understand the modulo function. And as a final point, I am not familiar with any important application of any number system other than base 10 and base 2 (Hex and Octal are just convenient representation used for a fundamentally binary application)

what about base 12 or base 60 (our systems used for time)?

 

[dighn]

just add the digits, the result digit is the remainder of result/base, and carry over (result - result_digit)/base

 

[chiwawa626]

Ok wow that really clears it up thanks guys. Although i do have one more question how would you multiply the two numbers ?

 

[dighn]

multiply like you would in base 10

eg

132
*23
------
= 132*3 + 132*20

2*3 = 6 but tat exceeds 4, 6/5 = 1, carry over one and remainder = 1
so on

so
132*3 = 1001
132*20 = 3140
then you add to get 4141

 

[chiwawa626]

Yeh i just started trying to do it after i posted, and it works

Thanks for all the help guys/gals

 

[jwells777]

Originally posted by: Hector13

Originally posted by: jwells777
Honestly, it is probably easier to convert to base 10, add, then convert back to the other base if you need to. And the answer to your sample question is 11141 (base 5) or 796 (base 10). If you really want to add in a given number system, you need to understand the modulo function. And as a final point, I am not familiar with any important application of any number system other than base 10 and base 2 (Hex and Octal are just convenient representation used for a fundamentally binary application)

what about base 12 or base 60 (our systems used for time)?

lol....That is why I didn't come out and say that no other system is useful...What's worse is that I am of course quite familiar with those and they are of course quite important. But it is not often that you really perform what I would call significant math in either system.

 

[sciencewhiz]

Originally posted by: jwells777
Honestly, it is probably easier to convert to base 10, add, then convert back to the other base if you need to.

But if he converted to base 10 and then back, he wouldn't get credit on his homework