/sci/ - Science & Math

This thread is now about shilling your favorite nonstandard notations. Pic related shows some examples of [math]{\rm \bf signed~digits}[/math]. Draw a line over a digit and the digit becomes negative. It can be useful as an intermediate form if you're doing arithmetic by hand. I find it a bit faster than borrowing once you get used to it, and formalizes a lot of the clever shortcuts like doing 9x by 10x-x (since 9 can be rewritten as [math]1\bar{1}[/math]). Another use: You can represent real numbers as streams of signed digits, and you can do arithmetic operations on them without getting stuck when the answer is close to or equal to a terminating decimal. For example, if you tried to multiply an ordinary digit stream representing [math]\sqrt{2}[/math] by itself, you'd never have enough input digits decide whether the output stream should start with 1.999... or 2.000... . With signed digits this is no problem; you can just output 2.000... confident you can just throw in a negative digit the answer turns out to be less than 2.