n complement of a number in hardware [closed]

Question

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.

Closed 9 years ago.

Do you know an algorithm or a way to find out the complement of a number in base N.?

      For example number 001112 which is in base 3 .

Thank you

Answer 1

For a number with k digits, subtract it from (N^k)_N (perform the subtraction in base N, of course).

Answer 2

For the definition of the complement see http://www.enggpedia.com/computer-engineering-encyclopedia/dictionary/dgital-logic-design/1603-complements-types-of-complements-radix-a-diminished-radix-complement.
In your example the complement is 3^6 - 001112(base 3) = (333333+1-001112)(base 3) = (332221+1)(base 3) = 332222.

EDIT:

The comments below are of course right. Sorry for posting such a wrong example. Let me try to reformulate what I wanted to say (and please correct me if I am wrong again):

Your example, expressed in base 3, is:

 1000000
- 001112
--------
= 221111  

The question is if a final 1 should be added.
If one has only unsigned numbers, there is no need to add a 1, but the complement does not have an arithmetic significance.
If one has signed numbers, the complement can be interpreted as a kind of the negative of the original number, but not as the negative itself. An example in base 2:
If n = 01101, the 1's complement of n is 10010. If we add both, the result is of course 11111 which is not zero. Thus, the 1's complement of n is NOT -n. But if we add a final 1, we get 00000, i.e. zero. Therefore the result of building the 1's complement and adding a 1 is called the 2's complement, and this CAN be interpreted as -n.
I assume the same holds true for any base.