# State diagrams

exequor
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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Antiphon
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.

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.

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?