Balanced Ternary - Computation

Computation

There were a few experimental Russian computers (e.g. Setun) in the early days of computing that were built with balanced ternary instead of binary. The notation has a number of computational advantages over regular binary. Particularly, the plus-minus consistency cut down the carry rate in multi-digit multiplication, and the rounding-truncation equivalence cut down the carry in the rounding program when we do a fraction operation.

And, the notation has a mumber of computational advantages over traditional ternary. Particularly, the one-digit multiplication table has no carries in balanced ternary, and the addition table has only two symmetric carries instead of three.

This notation has the property that the leading non-zero digit is the sign of the full number. To compare two numbers, simply compare digits from the most significant to the least significant. The direction of the magnitude compare of the first digits that are different is the direction of the magnitude compare of the full numbers.

A number is divisible by three if the last digit is zero. The quick test for even is the analog of the base ten divide-by-nine test: add up all the digits and repeat until you have a one-digit number; the number is even if the final sum is zero.