I haven't seen the article, but the idea is quite old -- from the 50s or 60s, at least. Jack Dennis played with it in the 60s, I know. An interesting question was whether all of the electrical gain and signal restoration could be concentrated in two inverters, using essentially passive diode logic everywhere else. This is the construction: Think in terms of the number of input variables that are on, rather than which ones. Let the inputs be A, B, C. Define 0, 1, 2, 3 as the logic variables counting how many inputs are true. Now: /A = 0 + 1 (C + B) + 2 BC /B = 0 + 1 (A + C) + 2 AC /C = 0 + 1 (A + B) + 2 AB Now, we just need to make the signals 0, 1, 2. AB + BC + CA = 2 + 3 invert this to give 0 + 1 A + B + C = 1 + 2 + 3, so (0 + 1) (A + B + C) = 1 ABC = 3, so 1 + ABC = (1 + 3) Invert this to give (0 + 2) (0 + 1) ( 0 + 2) = 0 (0 + 2) (2 + 3) = 2 Done. On Jan 5, 2006, at 11:24 PM, Bernie Cosell wrote:
On 1 Jan 2006 at 19:53, Lee Sallows wrote:
The article of mine Jim Propp is looking for is: A Curious New Result in Switching Theory, Math Intelligencer Vol 12 No 1, 1990 pp 21 - 32, about which, I can hardly refrain from adding, I recently received some complimentary remarks from Don Knuth.
Is this available online anywhere? /bernie\
-- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--
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