Question

Any integer can be represented in binary, octal, decimal, and hexadecimal. What are the limits on representing integers using unary or only having the 1 digit?

Answer 1

It is true that any integer can be represented in binary, octal, decimal, and hexadecimal.

For Eg- In binary 110 can represent 6, In Hecadecimal 32 can be represented by 20,etc

The limits on representing integers using unary or only having the 1 digit:-

1. We will need significantly more number of digits to represent a number.Eg. 6 can be represented by 110 in binary, but in unary we will have two use six 1s "111111".
2. It will be slower to compute using unary system, as more digits are needed to be calculated.
3. Unary system will be more expensive than other systems, due to large number of digits.
4. Ambiguity in representing zero. 0 is currently represented by an empty string. But in registers extra mechanisms might be needed to represent empty string.
5. Empty string is itself a character. By using both empty string and 1 for representation. The unary system is not truly unary i.e. it uses 2 characters. So this is an ongoing debate in the scientific community whether "unary systems exist or not?".