Archive for the 'Mathematics' Category

A day for pi

Tuesday, March 14th, 2006

Happy Pi Day!

Balanced Ternary

Tuesday, December 20th, 2005

I just ran across an article on balanced ternary notation, a ternary number system that uses -1, 0, and 1 for digits.

What makes balanced ternary so pretty? It is a notation in which everything seems easy. Positive and negative numbers are united in one system, without the bother of separate sign bits. Arithmetic is nearly as simple as it is with binary numbers; in particular, the multiplication table is trivial. Addition and subtraction are essentially the same operation: Just negate one number and then add. Negation itself is also effortless: Change every 1(overbar) into a 1, and vice versa. Rounding is mere truncation: Setting the least-significant trits to 0 automatically rounds to the closest power of 3.