ConwayLife.com

Posted: **March 22nd, 2015, 2:22 pm**

Here is a full adder implemented in Amsterdam* (otherwise known as Star Wars or 345/2/4). I'm posting this in its own thread rather than the main Star Wars thread because I have a specific goal for you in mind: try and derive a full explanation of how this works. The "compendium" I uploaded recently may help. Enjoy.

Code: Select all

x = 263, y = 112, rule = 345/2/4
6.A11.A15.A11.A$5.3A4.A4.3A4.A8.3A4.A4.3A4.A$6.A4.3A4.A4.3A8.A4.3A4.A
4.3A$6.A5.A5.A5.A9.A5.A5.A5.A$5.3A4.A4.3A4.A8.3A4.A4.3A4.A$6.A4.3A4.A
4.3A8.A4.3A4.A4.3A$6.A5.A5.A5.A9.A5.A5.A5.A11.A98.A$5.3A4.A4.3A4.A8.
3A4.A4.3A4.A10.3A96.3A$6.A4.3A4.A4.3A8.A4.3A4.A4.3A10.A98.A$6.A5.A5.A
5.A9.A5.A5.A5.A$5.3A4.A4.3A4.A8.3A4.A4.3A4.A15.A90.A$6.A4.3A4.A4.3A8.
A4.3A4.A4.3A13.3A88.3A$6.A5.A5.A5.A9.A5.A5.A5.A15.A90.A$5.3A4.A4.3A4.
A8.3A4.A4.3A4.A$6.A4.3A4.A4.3A8.A4.3A4.A4.3A$6.A5.A5.A5.A9.A5.A5.A5.A
31.A$5.3A4.A4.3A4.A8.3A4.A4.3A4.A30.3A$6.A4.3A4.A4.3A8.A4.3A4.A4.3A
30.A$6.A5.A5.A5.A9.A5.A5.A5.A101.A6.A15.A$5.3A4.A4.3A4.A8.3A4.A4.3A4.
A35.A11.A52.3A4.3A13.3A$6.A4.3A4.A4.3A8.A4.3A4.A4.3A33.3A9.3A52.A6.A
15.A$6.A5.A5.A5.A9.A5.A5.A5.A35.A9.2A.2A$5.3A4.A4.3A4.A8.3A4.A4.3A4.A
46.2A.2A61.A7.A$6.A4.3A4.A4.3A8.A4.3A4.A4.3A46.3A61.3A5.3A$6.A5.A5.A
5.A9.A5.A5.A5.A48.A63.A7.A$5.3A4.A4.3A4.A8.3A4.A4.3A4.A$6.A4.3A4.A4.
3A2.CBA3.A4.3A4.A4.3A2.CBA$12.A11.A3.CBA9.A11.A3.CBA64.A$69.A13.A38.
3A24.A$68.3A11.3A38.A24.3A$.A27.A27.A11.A11.2A.2A63.A$3A25.3A25.3A23.
2A.2A3.CBA$.A27.A27.A15.A9.3A4.CBA52.A$72.3A9.A38.A20.3A7.A$56.3C14.A
22.A25.3A20.A7.3A$55.C3.C32.A2.3A25.A28.2A.2A$55.5C31.3A.2A56.3A19.4C
$55.C3.C32.A3.A58.A19.C3.C$55.C3.C35.3A56.3A10.A7.4C$96.A13.A20.A23.A
10.3A6.C3.C$69.A39.3A18.3A32.2A.2A5.4C$68.3A39.2A.A17.A32.2A.2A$69.A
8.A31.A.3A50.3A9.A27.A27.A27.A$77.3A4.A25.2A.A21.A14.A2.A12.A9.3A25.
3A25.3A25.3A$67.A.2A7.A4.3A23.3A22.3A12.6A22.A27.A27.A27.A$66.6A12.A
25.A6.A17.A14.2A.A$67.A2.A45.3A4.A$117.A4.3A26.A18.A17.A11.A15.A11.A
15.A11.A$123.A26.3A16.3A10.A4.3A4.A4.3A8.A4.3A4.A4.3A8.A4.3A4.A4.3A$
151.A18.A10.3A4.A4.3A4.A8.3A4.A4.3A4.A8.3A4.A4.3A4.A$127.A54.A5.A5.A
5.A9.A5.A5.A5.A9.A5.A5.A5.A$126.3A30.A6.A15.A4.3A4.A4.3A8.A4.3A4.A4.
3A8.A4.3A4.A4.3A$74.A9.A42.A30.3A4.3A13.3A4.A4.3A4.A8.3A4.A4.3A4.A8.
3A4.A4.3A4.A$73.3A7.3A4.A56.A11.A6.A15.A5.A5.A5.A9.A5.A5.A5.A9.A5.A5.
A5.A$74.A9.A4.3A54.3A33.A4.3A4.A4.3A8.A4.3A4.A4.3A8.A4.3A4.A4.3A$84.A
5.A56.A33.3A4.A4.3A4.A8.3A4.A4.3A4.A8.3A4.A4.3A4.A$78.A4.3A4.A91.A5.A
5.A5.A9.A5.A5.A5.A9.A5.A5.A5.A$77.3A4.A4.3A17.A41.A30.A4.3A4.A4.3A8.A
4.3A4.A4.3A8.A4.3A4.A4.3A$78.A11.A17.3A39.3A28.3A4.A4.3A4.A8.3A4.A4.
3A4.A8.3A4.A4.3A4.A$109.A41.A30.A5.A5.A5.A9.A5.A5.A5.A9.A5.A5.A5.A$
149.2A.2A28.A4.3A4.A4.3A8.A4.3A4.A4.3A8.A4.3A4.A4.3A$69.A27.A15.A34.
7A26.3A4.A4.3A4.A8.3A4.A4.3A4.A8.3A4.A4.3A4.A$68.3A20.A4.3A4.A8.3A20.
A13.A3.A28.A5.A5.A5.A9.A5.A5.A5.A9.A5.A5.A5.A$69.A20.3A4.A4.3A8.A20.
3A45.A4.3A4.A4.3A8.A4.3A4.A4.3A8.A4.3A4.A4.3A$91.A11.A31.A45.3A4.A4.
3A4.A8.3A4.A4.3A4.A8.3A4.A4.3A4.A$65.A10.A2.A23.A78.A5.A5.A5.A9.A5.A
5.A5.A9.A5.A5.A5.A$64.3A8.6A22.2A26.A50.A4.3A4.A4.3A8.A4.3A4.A4.3A8.A
4.3A4.A4.3A$65.A10.A.2A7.A15.A26.3A48.3A4.A4.3A4.A8.3A4.A4.3A4.A8.3A
4.A4.3A4.A$86.3A14.A5.A21.A50.A5.A5.A5.A9.A5.A5.A5.A9.A5.A5.A5.A$78.A
8.A15.2A3.3A71.A4.3A4.A4.3A8.A4.3A4.A4.3A8.A4.3A4.A4.3A$77.3A7.A15.A
5.A71.3A4.A4.3A4.A8.3A4.A4.3A4.A8.3A4.A4.3A4.A$78.A7.3A14.A5.A72.A5.A
5.A5.A9.A5.A5.A5.A9.A5.A5.A5.A$87.A5.A8.3A3.3A71.A4.3A4.A4.3A8.A4.3A
4.A4.3A8.A4.3A4.A4.3A$65.3C24.3A8.A5.A71.3A4.A4.3A4.A8.3A4.A4.3A4.A8.
3A4.A4.3A4.A$64.C3.C24.A15.A72.A11.A15.A11.A15.A11.A$64.5C39.3A38.A$
64.C3.C40.A38.3A$64.C3.C13.A66.A$81.3A$10.A27.A27.A15.A70.A$9.3A25.3A
25.3A39.3C9.C4.4C24.3A$10.A27.A27.A11.A27.C3.C9.C3.C3.C24.A$77.3A26.
5C2.9C2.4C$78.A27.C3.C9.C3.C3.C$9.CBA9.A11.A3.CBA9.A11.A27.A11.A4.C3.
C8.C4.4C$9.CBA3.A4.3A4.A4.3A2.CBA3.A4.3A4.A4.3A25.3A4.A4.3A$14.3A4.A
4.3A4.A8.3A4.A4.3A4.A21.A5.A4.3A4.A11.3C5.3C2.C3.C2.3C2.C5.5C2.4C$15.
A5.A5.A5.A9.A5.A5.A5.A20.3A10.A5.A4.4C2.C3.C3.C3.C2.C.C2.C3.C.C5.C5.C
13.A$15.A4.3A4.A4.3A8.A4.3A4.A4.3A14.A5.A11.A4.3A11.2C4.C7.C3.C5.C5.
5C2.3C6.A2.3A5.A$14.3A4.A4.3A4.A8.3A4.A4.3A4.A14.3A15.3A4.A4.4C3.C6.C
3.C3.C3.C3.C.C5.C9.C4.3A.2A5.3A$15.A5.A5.A5.A9.A5.A5.A5.A15.A17.A16.
5C4.3C4.C4.3C2.5C.5C.4C6.A3.A6.A$15.A4.3A4.A4.3A8.A4.3A4.A4.3A100.3A$
14.3A4.A4.3A4.A8.3A4.A4.3A4.A11.A90.A$15.A5.A5.A5.A9.A5.A5.A5.A10.3A$
15.A4.3A4.A4.3A8.A4.3A4.A4.3A10.A$14.3A4.A4.3A4.A8.3A4.A4.3A4.A$15.A
5.A5.A5.A9.A5.A5.A5.A$15.A4.3A4.A4.3A8.A4.3A4.A4.3A$14.3A4.A4.3A4.A8.
3A4.A4.3A4.A$15.A5.A5.A5.A9.A5.A5.A5.A$15.A4.3A4.A4.3A8.A4.3A4.A4.3A$
14.3A4.A4.3A4.A8.3A4.A4.3A4.A$15.A5.A5.A5.A9.A5.A5.A5.A$15.A4.3A4.A4.
3A8.A4.3A4.A4.3A$14.3A4.A4.3A4.A8.3A4.A4.3A4.A$15.A5.A5.A5.A9.A5.A5.A
5.A$15.A4.3A4.A4.3A8.A4.3A4.A4.3A$14.3A4.A4.3A4.A8.3A4.A4.3A4.A$15.A
5.A5.A5.A9.A5.A5.A5.A$15.A4.3A4.A4.3A8.A4.3A4.A4.3A$14.3A4.A4.3A4.A8.
3A4.A4.3A4.A$15.A11.A15.A11.A!

*Amsterdam, not Star Wars, because it's fast bicycles all around. Also to avoid the trademark.

Posted: **April 16th, 2015, 11:46 pm**

I'm so glad we have some interesting stuff in this rule now! I thought it was aching for serious attention.

Posted: **May 10th, 2015, 1:45 am**

I tried to find a binary counter running at p128; this was the closest I got (it generates a Sierpiński triangle):

Code: Select all

x = 816, y = 82, rule = 345/2/4
812.A$811.3A$812.A2$796.A11.A$795.3A9.3A$794.2A.2A9.A$793.2A.2A$794.
3A$795.A4$813.A$812.3A$811.2A.2A$804.ABC3.2A.2A$804.ABC4.3A$812.A$.A
798.A$3A6.A51.A51.A51.A51.A51.A51.A51.A51.A51.A51.A51.A51.A51.A51.A
58.C2.3A2.A$.A6.3A49.3A49.3A49.3A49.3A49.3A49.3A49.3A49.3A49.3A49.3A
49.3A49.3A49.3A49.3A57.C3.2A.3A$9.A5.A36.A8.A5.A36.A8.A5.A36.A8.A5.A
36.A8.A5.A36.A8.A5.A36.A8.A5.A36.A8.A5.A36.A8.A5.A36.A8.A5.A36.A8.A5.
A36.A8.A5.A36.A8.A5.A36.A8.A5.A36.A8.A5.A36.A19.A3.A$14.3A34.3A12.3A
34.3A12.3A34.3A12.3A34.3A12.3A34.3A12.3A34.3A12.3A34.3A12.3A34.3A12.
3A34.3A12.3A34.3A12.3A34.3A12.3A34.3A12.3A34.3A12.3A34.3A12.3A34.3A
17.3A$15.A5.A30.A14.A5.A30.A14.A5.A30.A14.A5.A30.A14.A5.A30.A14.A5.A
30.A14.A5.A30.A14.A5.A30.A14.A5.A30.A14.A5.A30.A14.A5.A30.A14.A5.A30.
A14.A5.A30.A14.A5.A30.A14.A5.A30.A19.A$20.3A49.3A49.3A49.3A49.3A49.3A
49.3A49.3A49.3A49.3A49.3A49.3A49.3A49.3A49.3A$21.A26.A24.A26.A24.A26.
A24.A26.A24.A26.A24.A26.A24.A26.A24.A26.A24.A26.A24.A26.A24.A26.A24.A
26.A24.A26.A24.A26.A24.A26.A$47.3A49.3A49.3A49.3A49.3A49.3A49.3A49.3A
49.3A49.3A49.3A49.3A49.3A49.3A49.3A$25.A22.A28.A22.A28.A22.A28.A22.A
28.A22.A28.A22.A28.A22.A28.A22.A28.A22.A28.A22.A28.A22.A28.A22.A28.A
22.A28.A22.A28.A22.A$24.3A49.3A49.3A49.3A49.3A49.3A49.3A49.3A49.3A49.
3A49.3A49.3A49.3A49.3A49.3A$25.A51.A51.A51.A51.A51.A51.A51.A51.A51.A
51.A51.A51.A51.A51.A3$4.A51.A51.A51.A51.A51.A51.A51.A51.A51.A51.A51.A
51.A51.A51.A51.A$3.3A49.3A49.3A49.3A49.3A49.3A49.3A49.3A49.3A49.3A49.
3A49.3A49.3A49.3A49.3A49.3A$4.A51.A51.A51.A51.A51.A51.A51.A51.A51.A
51.A51.A51.A51.A51.A51.A5$27.A20.A30.A20.A30.A20.A30.A20.A30.A20.A30.
A20.A30.A20.A30.A20.A30.A20.A30.A20.A30.A20.A30.A20.A30.A20.A30.A20.A
30.A20.A$26.3A18.3A28.3A18.3A28.3A18.3A28.3A18.3A28.3A18.3A28.3A18.3A
28.3A18.3A28.3A18.3A28.3A18.3A28.3A18.3A28.3A18.3A28.3A18.3A28.3A18.
3A28.3A18.3A28.3A18.3A$27.A20.A30.A20.A30.A20.A30.A20.A30.A20.A30.A
20.A30.A20.A30.A20.A30.A20.A30.A20.A30.A20.A30.A20.A30.A20.A30.A20.A
30.A20.A2$23.A28.A22.A28.A22.A28.A22.A28.A22.A28.A22.A28.A22.A28.A22.
A28.A22.A28.A22.A28.A22.A28.A22.A28.A22.A28.A22.A28.A22.A28.A$22.3A
26.3A20.3A26.3A20.3A26.3A20.3A26.3A20.3A26.3A20.3A26.3A20.3A26.3A20.
3A26.3A20.3A26.3A20.3A26.3A20.3A26.3A20.3A26.3A20.3A26.3A20.3A26.3A
20.3A26.3A$23.A28.A22.A28.A22.A28.A22.A28.A22.A28.A22.A28.A22.A28.A
22.A28.A22.A28.A22.A28.A22.A28.A22.A28.A22.A28.A22.A28.A22.A28.A9$
737.A$736.3A$737.A5.A36.A$742.3A34.3A$743.A5.A30.A$748.3A$749.A26.A$
775.3A$753.A22.A$752.3A$753.A3$732.A51.A$731.3A49.3A$732.A51.A5$755.A
20.A$754.3A18.3A$755.A20.A2$751.A28.A$750.3A26.3A$751.A28.A!

Anyone want to try their hand at getting a p128 binary counter?

Posted: **November 28th, 2018, 7:33 am**

After several years I came back to Star Wars (I no longer have an aversion to calling it this) and found, after a day of struggling to close loops, this stable (no photon guns) serial Star Wars adder at p128:

Code: Select all

x = 193, y = 177, rule = 345/2/4
71.B.2C$71.B.2B$71.B.2A3$75.A2.A2.A2.A2.A2.A2.A2.A2.A$74.27A$75.A2.A
2.A2.A2.A2.A2.A2.A2.A4$74.A2.A2.A2.A2.A2.A2.A2.A2.A$73.27A$74.A2.A2.A
2.A2.A2.A2.A2.A2.A4$75.A2.A2.A2.A2.A2.A2.A2.A2.A$74.27A$75.A2.A2.A2.A
2.A2.A2.A2.A2.A4$74.A2.A2.A2.A2.A2.A2.A2.A2.A$73.27A$74.A2.A2.A2.A2.A
2.A2.A2.A2.A3$71.B$71.B$71.B3$75.A2.A2.A2.A2.A2.A2.A2.A2.A$74.27A$75.
A2.A2.A2.A2.A2.A2.A2.A2.A4$74.A2.A2.A2.A2.A2.A2.A2.A2.A$73.27A$74.A2.
A2.A2.A2.A2.A2.A2.A2.A4$75.A2.A2.A2.A2.A2.A2.A2.A2.A$74.27A$75.A2.A2.
A2.A2.A2.A2.A2.A2.A$63C$C61.C$C4.A56.C$C3.3A55.C11.A2.A2.A2.A2.A2.A2.
A2.A2.A$C4.A56.C10.27A$C17.A39.A3.C11.A2.A2.A2.A2.A2.A2.A2.A2.A$C8.A
7.3A37.3A2.C$C7.3A5.2A.2A35.2A.2A.C$C8.A7.3A35.2A.2A2.C8.B.2C$C16.A
38.3A3.C8.B.2B$C15.3A38.A4.8C.B.2A.3C$C16.A60.C$C66.A10.C$C65.3A6.A2.
C$C66.A6.3A.C$C74.A2.C$C74.A2.C$C73.2A2.C$C74.A2.C$C67.A6.A2.C$C66.3A
4.3A.C$C31.C3.3C3.3C23.A6.A2.C$C30.2C2.C3.C.C3.C32.C$C31.C2.C5.C3.C
25.A6.C$C31.C2.4C3.3C25.3A5.C$C31.C2.C3.C.C3.C25.A6.C$C31.C2.C3.C.C3.
C32.36C$C30.3C2.3C3.3C68.C$C102.A9.C$C101.3A8.C$C72.A25.A3.A6.A2.C$C
8.A62.3A23.3A.2A5.3A.C$C2.A4.3A62.A25.A2.3A5.A2.C$C.3A4.A93.A9.C$C2.A
73.A35.C$C75.3A24.11C$10C67.A25.C$9.C4.A88.C$9.C3.3A87.C$9.C4.A88.C$
9.C2.3A88.C$9.C.2A.2A64.A22.C$9.C2.3A7.A56.3A21.C$9.C3.A7.3A56.A22.C$
9.C12.A29.A50.C$9.C36.A4.3A23.A6.A18.C$9.C16.A18.3A4.A23.3A4.3A17.C$
9.C15.3A12.A5.A5.A24.A6.A18.C$9.C16.A7.A4.3A4.A4.3A30.A18.C$9.C23.3A
4.A4.3A4.A30.2A18.C$9.18C7.A11.A11.A25.A18.C$26.C30.3A24.A18.C$26.C
31.A17.A6.3A17.C$26.C31.A16.3A6.A18.C3.A27.A27.A27.A$26.C30.2A11.A5.A
26.C2.3A25.3A25.3A25.3A$26.C31.A10.3A31.C3.A27.A27.A27.A$26.C31.A11.A
14.B17.C$26.C30.2A11.A14.B$26.C31.A10.3A13.B14.A2.C14.A11.A15.A11.A
15.A11.A$26.C31.A11.A28.3A.C8.A4.3A4.A4.3A8.A4.3A4.A4.3A8.A4.3A4.A4.
3A$26.C30.2A11.A29.A10.3A4.A4.3A4.A8.3A4.A4.3A4.A8.3A4.A4.3A4.A$26.C
31.A10.3A31.C8.A5.A5.A5.A9.A5.A5.A5.A9.A5.A5.A5.A$26.C31.A11.A18.A6.A
6.C8.A4.3A4.A4.3A8.A4.3A4.A4.3A8.A4.3A4.A4.3A$26.C30.2A11.A17.3A4.3A
5.C7.3A4.A4.3A4.A8.3A4.A4.3A4.A8.3A4.A4.3A4.A$26.C31.A10.3A17.A6.A6.C
8.A5.A5.A5.A9.A5.A5.A5.A9.A5.A5.A5.A$26.C31.A11.A32.C8.A4.3A4.A4.3A8.
A4.3A4.A4.3A8.A4.3A4.A4.3A$26.C30.2A11.A32.C7.3A4.A4.3A4.A8.3A4.A4.3A
4.A8.3A4.A4.3A4.A$26.C31.A10.3A31.C8.A5.A5.A5.A9.A5.A5.A5.A9.A5.A5.A
5.A$26.C31.A11.A32.C8.A4.3A4.A4.3A8.A4.3A4.A4.3A8.A4.3A4.A4.3A$26.C
30.2A11.A32.C7.3A4.A4.3A4.A8.3A4.A4.3A4.A8.3A4.A4.3A4.A$26.C31.A10.3A
31.C8.A5.A5.A5.A9.A5.A5.A5.A9.A5.A5.A5.A$26.C31.A5.A5.A32.C8.A4.3A4.A
4.3A8.A4.3A4.A4.3A8.A4.3A4.A4.3A$26.C30.3A3.3A4.A32.C7.3A4.A4.3A4.A8.
3A4.A4.3A4.A8.3A4.A4.3A4.A$26.C31.A5.A4.3A31.C8.A5.A5.A5.A9.A5.A5.A5.
A9.A5.A5.A5.A$26.C43.A32.C8.A4.3A4.A4.3A8.A4.3A4.A4.3A8.A4.3A4.A4.3A$
26.C64.A2.A8.C7.3A4.A4.3A4.A8.3A4.A4.3A4.A8.3A4.A4.3A4.A$26.C63.6A7.C
8.A5.A5.A5.A9.A5.A5.A5.A9.A5.A5.A5.A$26.C4.A59.A.A.2A6.C8.A4.3A4.A4.
3A8.A4.3A4.A4.3A8.A4.3A4.A4.3A$26.C3.3A60.3A7.C7.3A4.A4.3A4.A8.3A4.A
4.3A4.A8.3A4.A4.3A4.A$26.C4.A62.A8.C8.A5.A5.A5.A9.A5.A5.A5.A9.A5.A5.A
5.A$26.C2.3A71.C8.A4.3A4.A4.3A8.A4.3A4.A4.3A8.A4.3A4.A4.3A$26.C.2A.2A
.70C7.3A4.A4.3A4.A8.3A4.A4.3A4.A8.3A4.A4.3A4.A$26.C2.3A2.C77.A5.A5.A
5.A9.A5.A5.A5.A9.A5.A5.A5.A$26.C3.A3.C77.A4.3A4.A4.3A8.A4.3A4.A4.3A8.
A4.3A4.A4.3A$26.C7.C76.3A4.A4.3A4.A8.3A4.A4.3A4.A8.3A4.A4.3A4.A$26.9C
77.A11.A15.A11.A15.A11.A2$40.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A
2.A$39.45A$40.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A4$39.A2.A2.A
2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A2.A$38.45A$39.A2.A2.A2.A2.A2.A2.A2.A
2.A2.A2.A2.A2.A2.A2.A3$82.2A.B$82.2B.B$82.2C.B3$58.A2.A2.A2.A2.A2.A2.
A2.A2.A$57.27A$58.A2.A2.A2.A2.A2.A2.A2.A2.A4$57.A2.A2.A2.A2.A2.A2.A2.
A2.A$56.27A$57.A2.A2.A2.A2.A2.A2.A2.A2.A4$58.A2.A2.A2.A2.A2.A2.A2.A2.
A$57.27A$58.A2.A2.A2.A2.A2.A2.A2.A2.A4$57.A2.A2.A2.A2.A2.A2.A2.A2.A$
56.27A$57.A2.A2.A2.A2.A2.A2.A2.A2.A3$82.2A.B$82.2B.B$82.2C.B!

It is also slightly smaller than the adder at the top of this thread and takes 168 instead of 256 ticks from marked input to marked output. Because it is stable, it can easily be adapted to larger periods.

Let the two inputs be A and B. There is a loop at the left holding the carry bit C, with an AND gate embedded within it. The computation C' = ((A XOR B) AND C) XOR (A AND B) is performed to update the carry bit, which you may easily verify is correct – figuring out how to route A AND B into the outermost XOR in time was the hardest part. The right side of the adder is another XOR gate that yields the output S = (A XOR B) XOR C, where A XOR B comes from the "other side" of the computation performed to update C (the XOR gate is two-sided).

Posted: **November 28th, 2018, 11:41 am**

Welcome back, Freywa.

Posted: **November 28th, 2018, 5:47 pm**

This full adder may be useful:

Code: Select all

x = 171, y = 192, rule = 345/2/4
87.C.C.C2$87.C2$87.C2$87.C2$87.C.C.C3$89.C$89.C$89.C$89.C$89.C$89.C$
89.C$89.C$89.C$89.C$89.C$89.C$89.C$87.C.C.C$88.3C$89.C17$88.2B$88.2A
49$C.C2$C3.C2$C.C.C18.C.C.C2$C3.C18.C3.C2$C.C20.C.C.C2$2.C20.C3.C$2.C
$2.C20.C3.C$2.C$2.C22.C$2.C22.C$2.C22.C45.A$2.C22.C44.3A$2.C22.C45.A
83.A$2.C22.C128.3A$2.C22.C14.A114.A$C.C.C20.C13.3A15.A19.A6.A8.A6.A6.
A6.A$.3C21.C14.A15.3A4.A6.A5.3A4.3A6.3A4.3A4.3A4.3A35.A$2.C22.C25.A5.
A4.3A4.3A5.A6.A8.A6.A6.A6.A12.A11.A10.3A$25.C18.A5.3A10.A6.A6.A6.A8.A
6.A6.A6.A6.A4.3A4.A4.3A10.A$25.C17.3A5.A24.3A4.3A6.3A4.3A4.3A4.3A4.3A
4.A4.3A4.A$23.C.C.C16.A32.A6.A8.A6.A6.A6.A6.A11.A$24.3C$25.C$12.BA$
12.BA$69.A$68.3A$69.A$31.BA$31.BA40.A$45.A26.3A$44.3A26.A$45.A2$49.A$
48.3A24.A$49.A24.3A53.A$75.A53.3A$130.A2$99.A$74.A23.3A15.A$73.3A23.A
15.3A4.A6.A$74.A35.A5.A4.3A4.3A20.A3.A$103.A5.3A10.A6.A20.7A$102.3A5.
A40.2A.2A$103.A49.A$152.3A$153.A$71.A$70.3A76.A$71.A56.A19.3A$127.3A
19.A$60.A6.A60.A$59.3A4.3A19.A$60.A6.A19.3A42.A$88.A15.A26.3A$103.3A
26.A$84.A19.A$83.3A$49.A15.A18.A23.A39.A$48.3A13.3A40.3A24.A12.3A$49.
A15.A42.A24.3A12.A$134.A34.A$45.A23.A74.A17.A5.3A$44.3A21.3A72.3A15.
3A5.A$45.A23.A74.A17.A$133.A$132.3A$133.A6$130.A$129.3A$130.A$169.A$
119.A6.A35.A5.3A$118.3A4.3A33.3A5.A$119.A6.A35.A5$108.A15.A$107.3A13.
3A$108.A15.A2$104.A23.A$103.3A21.3A$104.A23.A!

The outputs are separate, so it can do ripple-carry.

Posted: **November 29th, 2018, 12:18 am**

AforAmpere wrote:The outputs are separate, so it can do ripple-carry.

Not very desirable if you want to build a reasonably fast Wireworld-style computer, because (as is well-known) ripple carry adders suffer long propagation times.

Posted: **December 1st, 2018, 10:40 am**

As it turns out, a true binary counter wasn't that hard:

Code: Select all

x = 492, y = 115, rule = 345/2/4
490.A$489.3A$490.A$489.ABC$486.A$107.ABC125.ABC125.ABC119.3A$107.ABC
125.ABC125.ABC120.A$2.A$.3A$2A.A.A$.6A$2.A2.A5$481.A2.A$480.6A$7.A
473.A.A.2A$6.3A474.3A$7.A476.A$5.3A$4.2A.2A$5.3A$6.A6$490.A$489.3A$
490.A$489.ABC$486.A$363.ABC119.3A$363.ABC120.A$258.A$257.3A$256.2A.A.
A$257.6A$258.A2.A5$481.A2.A$480.6A$263.A217.A.A.2A$262.3A218.3A$263.A
220.A$261.3A$260.2A.2A$261.3A$262.A6$490.A$489.3A$490.A$489.ABC$486.A
$485.3A$486.A$386.A$385.3A$384.2A.A.A$385.6A$386.A2.A5$481.A2.A$480.
6A$391.A89.A.A.2A$390.3A90.3A$391.A92.A$389.3A$388.2A.2A$389.3A$390.A
6$477.A$476.3A$477.A$476.ABC$473.A$472.3A$473.A$437.A$436.3A$435.2A.A
.A$436.6A$437.A2.A5$468.A2.A$467.6A$442.A25.A.A.2A$441.3A26.3A$442.A
28.A$440.3A$439.2A.2A$440.3A$441.A!

Posted: **December 1st, 2018, 4:14 pm**

Freywa wrote:Not very desirable if you want to build a reasonably fast Wireworld-style computer, because (as is well-known) ripple carry adders suffer long propagation times.

However, (as is well-known), many commonly used pieces of adding circuitry use ripple-carry as part of their circuitry. Carry-save adders can be pretty useful at reducing delays, and they use RCA circuitry, hence being able to construct an RCA may be useful in certain cases. Another adder, the carry-increment adder, has also been shown to be fairly efficient, and it also uses RCAs. And carry-select adders use them too. My point is that being able to easily construct a RCA can actually be fairly useful if your concern is propagation. This is not to say that my adder is incredibly efficient, but RCAs are a pretty important part of efficient adding circuits, even though they themselves are not incredibly efficient, and constructing those more basic circuits can be useful for better ones.

ConwayLife.com

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