Iggy et al., Yep. Interestingly there is an alternate formulation known as the *Balanced* trinary number system. (One of the folks around here wants to label it "BaTeNuS".) The idea is that the digits, rather than being 0, 1, 2 for each place value, are (-1), 0, 1, meaning subtract, don't do either, or add the place value in which that digit appears. For convenience I'll write (-1) as "n" below, though in (LaPlace's?) original work it was written as 1 with an overstrike. Decimal Batenus Explanation ... -9 n00 (-1) * 3^2 + 0 + 0 -8 n01 (-1) * 3^2 + 0 + 1 * 3^0 -7 n1n (-1) * 3^2 + 1 * 3^1 + (-1) * 3^0 -6 n10 (-1) * 3^2 + 1 * 3^1 + 0 -5 n11 (-1) * 3^2 + 1 * 3^1 + 1 * 3^0 -4 nn 0 + (-1) * 3^1 + (-1) * 3^0 -3 n0 0 + (-1) * 3^1 + 0 -2 n1 0 + (-1) * 3^1 + 1 * 3^0 -1 n 0 + 0 + (-1) * 3^0 0 0 0 + 0 + 0 1 1 0 + 0 + 1 * 3^0 2 1n 0 + 1 * 3^1 + (-1) * 3^0 3 10 0 + 1 * 3^1 + 0 4 11 0 + 1 * 3^1 + 1 * 3^0 5 1nn 1 * 3^2 + (-1) * 3^1 + (-1) * 3^0 6 1n0 1 * 3^2 + (-1) * 3^1 + 0 7 1n1 1 * 3^2 + (-1) * 3^1 + 1 * 3^0 ... you get the idea. Notice that negative numbers are built in - no need for an additional (-) symbol leading a number. Also notice that to negate a number, you just negate each digit. Fractions, addition tables, etc. are left as an exercise for the reader. This system is great if you have a balance beam and want a minimum number of known weights. To get an (n), you put a known weight on the same side as the object being weighed, while to get a (1), put that weight on the opposite side. With 4 weights, (27, 9, 3, 1) you can generate every integer weight from -40 to 40 - try that with a decimal set of weights (or binary, for that matter). The problem I see with putting either Batenus or trinary in silicon (or gallium arsenide, etc.) is that all the electric technologies I know of are fundamentally binary. On/off, charge stored vs. not stored, current flowing vs. not flowing, etc. You need two binary bits (4 states) to hold a trinary digit (3 states), so there's a 33% loss. Even ignoring this, you only get a 50% increase in information capability and processing speed at best. Would you rather rebuild your computers from the gate level up, including all of the software, or just wait 6 months for the semiconductor industry to get you the 50% speedup in binary? However, I do notice that SQUID circuits, and some other superconducting phenomena, might well be made to work in a trinary fashion (no current, current circulating left, current circulating right). If so, that might make Batenus or trinary pretty interesting again. Am I Off-topic if I'm 10 years into the future? :-) - Mark Linc, Calculating in Batenus is as easy as 1,1n,10