Single quotes for single characters and double quotes for double?

I’ve been under the impression that you use single quotation marks for single characters or numerals.

Usage: ‘1’ or ‘a’ and not “1” or “a”.

(You would double quotation marks for anything longer than one character.)

Is this a correct assumption?

Note: I’m aware that there are topics that discuss the usage of both single and double quotation marks, but my question is intended to be a specific as possible as it may benefit others here.

No it is not.

I believe you probably got that impression, directly or indirectly, from the programming language C, which does in fact have that as a rule. However, human languages are not programming languages. We don't really have an overwhelming need as people to differentiate a single letter from a string that happens to have only a single character in it.

In the U.S. (at least according to the Chicago Manual of Style), the only thing you're supposed to use single quotes for is quotations within quotations. This strikes me as a grievous underuse of a potentially useful punctuation mark. I would be interested in knowing what the British system is.

Grammar Girl has a nice article on this question.