# State diagrams

Ok, I am currently taking a course where you have to draw state diagrams to represent functions in different bases. the function is $$2x_{1}+x_{2}$$. When you add two numbers regardless of the base you have a sum (least significant digit) and a carry. Now in base one, is it possible to have a carry greater than "1" since all you are dealing with is "0"s and "1"s?

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exequor said:
Ok, I am currently taking a course where you have to draw state diagrams to represent functions in different bases. the function is 2(x1) + (x2). When you add two numbers regardless of the base you have a sum (least significant digit) and a carry. Now in base one, is it possible to have a carry greater than "1" since all you are dealing with is "0"s and "1"s?

You must mean base 2. In base one, you only have one digit, 0.

No, the carry is always a 1.

01 + 01 = 10. The carry was a "1" into the second slot.

Astronuc
Staff Emeritus
I agree with Antiphon, I think you mean binary (base 2). I have not heard of a unary base being used.

Definition of unary base (from dictionary.com) - <data, humour> Base one. A number base with only one digit, namely zero, and which can therefore only be used to express the number zero. Attempting to add one to zero results in an infinite sequence of carries. Numbers in unary notation can be represented particularly efficiently however since each digit requires no storage.

Averagesupernova
Gold Member
Exequor, think of it this way. Do you ever carry anything larger than 9 in base 10 system? You know the answer of course, and we never carry 0 (duh) soooooo, there is only one thing in binary we ever carry and that is 1.

Oh yea, I meant base two. :D

The thing is the class is "digital logic" right, and using my own logic I know that there can not be a carry of "2" in base two. I mentioned it to the professor and he said that you can have a carry of any size... to me it is a matter of confusing bases and the way that we use them because I think that it is a base ten thing. I just had to ask the question here to ensure that I was not the only "stupid" person that thought the largest carry in base two is "1" and the highest carry in base five is "4".

If the function was $$3x_{1}+x_{2}$$ and you got something like 4 you convert that to base two... 100 your sum would be "0" and your carry would be "100" right?

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