Ternary has interesting advantages, but (to maintain equivalent noise margings) dissipates more power than binary, since it needs similar voltage differences between each value, and the energy is proportional to the voltage squared. Binary is best from a power standpoint, and this is completely dominant in today's technologies (until we start working with reversible, dissipationless computers). On Dec 6, 2013, at 2:13 PM, Adam P. Goucher wrote:
Nice. These problems are circumvented by the use of an odd radix, such as ternary (base-3). Balanced ternary has the beautiful property that rounding and truncation are precisely the same operation, and it's very easy to represent and compute negative numbers. I seem to recall that the Russians even had a balanced ternary computer in the mid-20th-century, called Setun or something like that.
Sincerely,
Adam P. Goucher
----- Original Message ----- From: Eugene Salamin Sent: 12/06/13 07:05 PM To: math-fun Subject: Re: [math-fun] There must be something wrong with Mathematica's Round function--
Every system of rounding has some arbitrary convention for dealing with 5. I like the convention that was used in numerical tables, in which a least significant digit of 5 that was rounded upward had an overbar over the 5 to signal that the number should be rounded downward in a further rounding. For example, the number 0.12349 in a 4-place table is written as 0.1235 with an overbar over the 5. Then if someone wants a 3-place value, they know to use 0.123 rather than 0.124.
-- Gene
________________________________ From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Friday, December 6, 2013 10:44 AM Subject: Re: [math-fun] There must be something wrong with Mathematica's Round function--
OK, that would explain Mathematica's reasoning.
But why? According to what system of rounding?
--Dan
On 2013-12-06, at 9:36 AM, Adam P. Goucher wrote:
Half-integers are rounded to the nearest even integer.
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