Spencer-Brown Counter

Heater.

Whilst discussing the meaning of pi and hence the existence or not of mathematical objects/concepts I took another look at the work of George Spencer Brown, his famous work "The Laws of Form".

http://www.lawsofform.org/
http://en.wikipedia.org/wiki/Laws_of_form

In doing so I stumbled across a binary counter, or at least divide by two, stage that he devised. It uses only NOR gates and is quite unlike any divider stage I have seen before.

http://www.lawsofform.org/counter/index.html

Here is my rendition of it in KiCad.

Anyone out there got a logic simulator to quickly verify this works as advertised?

Edit: Updated schematic with annotated signals.

Vern

Spice is available for linux and its free

Heater.

Vern,

I have SwitcherCAD (LTSpice) running under Wine on Linux. It never occurred to me to use it for logic simulation:)

Anyway I updated the schematic in the first post with labelled signals. and the simulated the thing with a little C program. Results show that it does indeed divide by two.

The more I look at it the more I think it actually just a Master-Slave JK Flip-Flop drawn in an odd manner.

Spencer-Brown counter.
IN A B C D E F G H
0  0 0 0 0 1 0 0 1
0  0 1 0 0 1 0 0 1
0  0 1 0 0 1 0 0 1
0  0 1 0 0 1 0 0 1
1  0 1 0 0 0 0 1 0
1  0 1 0 1 0 0 1 0
1  0 1 0 1 0 0 1 0
1  0 1 0 1 0 0 1 0
0  1 0 0 1 0 1 0 0
0  1 0 0 1 0 1 0 0
0  1 0 0 1 0 1 0 0
0  1 0 0 1 0 1 0 0
1  0 0 1 0 0 1 0 1
1  0 0 1 0 0 1 0 1
1  0 0 1 0 0 1 0 1
1  0 0 1 0 0 1 0 1
0  0 0 0 0 1 0 0 1
0  0 1 0 0 1 0 0 1
0  0 1 0 0 1 0 0 1
0  0 1 0 0 1 0 0 1
1  0 1 0 0 0 0 1 0
1  0 1 0 1 0 0 1 0
1  0 1 0 1 0 0 1 0
1  0 1 0 1 0 0 1 0
0  1 0 0 1 0 1 0 0
0  1 0 0 1 0 1 0 0
0  1 0 0 1 0 1 0 0
0  1 0 0 1 0 1 0 0
1  0 0 1 0 0 1 0 1
1  0 0 1 0 0 1 0 1
1  0 0 1 0 0 1 0 1
1  0 0 1 0 0 1 0 1
0  0 0 0 0 1 0 0 1
0  0 1 0 0 1 0 0 1
0  0 1 0 0 1 0 0 1
0  0 1 0 0 1 0 0 1
1  0 1 0 0 0 0 1 0
1  0 1 0 1 0 0 1 0
1  0 1 0 1 0 0 1 0
1  0 1 0 1 0 0 1 0
0  1 0 0 1 0 1 0 0
0  1 0 0 1 0 1 0 0
0  1 0 0 1 0 1 0 0
0  1 0 0 1 0 1 0 0
1  0 0 1 0 0 1 0 1
1  0 0 1 0 0 1 0 1
1  0 0 1 0 0 1 0 1
1  0 0 1 0 0 1 0 1

Beau Schwabe

Hate to disappoint you, but this is just a D-Flip-Flop configured as a divide by 2.


In a D-Flip-Flop, there are two outputs, 'Q' and 'Q-Not'

If you take the 'Q-Not' and feed it to the 'D' input and use the 'Clock' as your data/frequency input, then 'Q' or even 'Q-Not' will show up as having half of the input frequency.

Here is an animation. It's the same schematic, just drawn differently.
http://www.youtube.com/watch?v=9nCg1eSnVTE

Heater.

Beau,

No need to worry about disappointing me, after starring at it for a while I came to the same conclusion.

It's just that Spencer-Brown had an odd way of drawing it. Still, I don't think the logic symbols were so standardized when he did it back in the early 60's and perhaps the nomenclature of the various flip-flop types as we know today was not in place either.

Well, OK I said JK flip-flop, almost same:)