phillips@cs.ubc.ca (George Phillips) (02/28/90)
About a week ago, Ian Woollard <irw@stl.stc.co.uk> sent me a
wonderful XOR gate he created:
........=
........=
.......===
.......=.=
===-#===.===#-==
.......===
And then used (A^B)^A == B to do a very good wire crossing.
BTW: my wire crossings _do_ work, but who cares with this around:
...=.....=
...=.....=
..===...===
..=.=...=.=
.==.==.==.==
=.===.=.===.=
=.....=.....=
=....===....=
.=...=.=...=
..=.==.==.=
...=.===.=
...#.....#
...-.....-
While trying to understand the XOR gate, I realized that one of the
tricks was to make each incoming pulse cancel themselves. I used this
idea to make a faster AND gate:
............==
...........=..=#-====-===#-
......==..===
.....=..=..=..=.=#-===#-====-
....===..==.==.=
....==.........=
====..=========
I don't know if it's me or wireworld, but none of the AND gates are
symmetric. Hmmmm. Maybe someone will surprise me -- getting new
patterns from the net is almost as much fun as building them yourself.
George Phillips phillips@cs.ubc.ca {alberta,uw-beaver,uunet}!ubc-cs!phillipsdeath@watcsc.waterloo.edu (Trevor Green) (03/01/90)
In article <6937@ubc-cs.UUCP> phillips@cs.ubc.ca (George Phillips) writes: >About a week ago, Ian Woollard <irw@stl.stc.co.uk> sent me a >wonderful XOR gate he created: ..I... .====. .=..=O .====. ..I... Transit: 3 IBI: 5 Size: 6x5 I like it. This is "the" XOR gate. >And then used (A^B)^A == B to do a very good wire crossing. >BTW: my wire crossings _do_ work, but who cares with this around: The first half of that BTW is still open to debate. The second half is unconditionally true and makes the debate irrelevant. ........... .....==.... ....=..=... ...=..====. .I=...=..=O ..=...====. .====..=... .=..===.... .====..=... ..=...====. .I=...=..=O ...=..====. ....=..=... .....==.... ........... Transit: 9 IBI: 5 Size: 11x15 I tried to "simplify" this (it still looks too open for me) and replaced the final XORs with much simpler structures. This also entailed adding two diodes and I wound up upping the IBI to 11 with the size and transit time remaining about the same. This appears to be an excellent design. I'll see if I can improve on it, but I think that this is *the* A^B^A design. It'll be a completely different design that beats it. >While trying to understand the XOR gate, I realized that one of the >tricks was to make each incoming pulse cancel themselves. I used this >idea to make a faster AND gate: > >............== >...........=..=#-====-===#- >......==..=== >.....=..=..=..=.=#-===#-====- >....===..==.==.= >....==.........= >====..========= Now, George, you're making me feel like a tinker to your artist. This one looked a little sloppy again, so I "fixed" it. (Believe it or not, the design below is "topologically" identical to the one above, except for one inconsequential change.) .I..... ..=.... .===... ..=.... I=.=... .=..=.. .=.===. .=..=.. ..==.O. Transit: 7 IBI: 5 (again!) Size: 7x9 >I don't know if it's me or wireworld, but none of the AND gates are >symmetric. Hmmmm. Maybe someone will surprise me -- getting new >patterns from the net is almost as much fun as building them yourself. My original AND gate was symmetric - double each input, XOR the middle two and then XOR again for the final output (more or less). ................ ..=====......... .=.....====.==.. .=..==.....=..=. .=.==.=...===.=. I.=.==.==..=..=. ........===..==O I.=.==.==..=..=. .=.==.=...===.=. .=..==.....=..=. .=.....====.==.. ..=====......... ................ Then I realised I could do without one of the doubled lines. ............. ...==........ ..==.=....... I=.==.==..... .......===... I..==.==..=.. .===.=...===. .=.==.....=.. .=....====.O. ..====....... ............. With the better XOR posted above, I have improved it once again, but it doesn't hold a candle to George's: .I........ ..=....... .====..... .=..===... .====..=.. ..=...===. .I.=...=.. ...=..=.O. ....=.=... .....=.... .......... Transit: 9 IBI: 5 Size: 10x11 The reason for the inefficiency compared to George's AND is that the XOR can be replaced by the other doohickey (the "implication" one (a&~b)...what'll we call it?) for an increase in through speed and decrease in size (amazing how often one follows the other in wireworld). >George Phillips phillips@cs.ubc.ca {alberta,uw-beaver,uunet}!ubc-cs!phillips Trevor Green death@csc.waterloo.edu watmath!maytag!watcsc!death