A few months ago, I read that a new philosophy called "The Laws of Form" could help you design a D flip-flop with a smaller number of gates.THAT reminded me of a trip I took 20 years ago, during which I actually did design a D flip-flop myself. I was working with some guys at Amelco, in Mountain View, Calif., on the industry's first 12-bit ADC IC, and I wanted to make a small, compact D flip-flop. I tried to do a design on the west-bound plane, but my efforts were utterly useless. I looked at the Design Rules, and I could not begin to design a layout for a D flip-flop. I did not know how to start.

Then when I got to see our collaborators, I took a look at their layout. OHHH, that's what a flip-flop layout looks like. I studied their design and took a copy back to my motel room. That night, after I comprehended their good layout, I designed a better layout that was not only 12% smaller, but 20% faster. We "analog" guys get the privilege of studying other peoples' best efforts, and if we can improve on them, we're considered wise. In this case, my cell was smaller and narrower, so a cascade of 12 of them would be a more compact block. Also, the delay to the Q-bar output was worse, but the delay to the Q output was smaller, so the ripple counter would have less delay during a ripple carry such as from (0111 1111 1111) to (1000 0000 0000).

The next day, when the Amelco guys looked at my best layout, they figured out a way to improve my layout by another 3% decrease in cell area. I then looked at their latest effort, and conceded that I could make no more improvement.

We built the circuit, and it worked the first time. We got it into production in 1975, and we sold some. (Note, all previous converters of this much resolution were designed to be digital voltmeters, putting out their drive to LED segments. This was the first one designed to interface with 12 lines to do a straight 12-bit binary output, coded as an ADC.)

I haven't done much design on flip-flops since that time, but the world doesn't need me to design flip-flops. I heard somewhere that there are 10,000 different designs for a 2-input NOR gate, each one slightly different. With that many gates, who needs me?

When I found out that you could use "The Laws of Form" to make a "better" flip-flop, I got curious. Could you really do better than the best efforts of designers over the last 30 years? Oh, yes, "The Laws of Form" showed how you could make a T flip-flop (divide-by-2 circuit) with only six gates, instead of the usual nine. WELL, that sounded like a little progress. BUT, since the guy who drew this to my attention made some "fuzzy" comments, I was prepared to be skeptical. Skeptical? Who, me?

I studied the proposed design for the "new, improved" flip-flop. Yes, there were only six gates----but each gate was a 3-input gate. Now, a CMOS inverter needs only two transistors, and can respond fairly fast. But a CMOS 3-input gate requires you to use six transistors, so it's definitely not as fast. In fact, a flip-flop that needs six 3-input gates will be much larger and slower than a conventional one that needs nine 2-transistor gates.

NOW, I'm in favor of trying out new concepts. If a novel approach really gives better results overall, hey, that's great. But if a new scheme merely has fewer gates, but more transistors, more area, and slower response, I can't get very enthusiastic. Further, as a friend pointed out, that 6-gate flip-flop isn't really new, since TI published that circuit more than 10 years ago. And it has few gates, which makes it hard to test....

If you want to build a flip-flop using just six transistors, as one engineer claims to have done, well, yes, you can do that, but it won't have the low-power advantages of CMOS. That sounds like RTL (resistor-transistor logic) to me, and hardly anybody uses RTL these days. The resistors get too bulky. It's transistors that are cheap, and resistors that are bulky and expensive.

George Spencer-Brown, the developer of the Laws of Form, is quoted as saying that when he began working as an engineer, he "realized the tools with which engineers worked were totally inadequate."

Spencer-Brown continues, "I gave a talk recently to engineers at Bell Labs ... but ... some time after my talk, they came to me and showed me a circuit they had designed using my principles, but it had three times the number of transistors that it needed. It seems I am the only engineer who can do it properly."Yeah, everybody's out of step with Johnny.

The Laws of Form claim to introduce "imaginary logical values" for circuits with feedback. "Armed with these imaginary values, digital engineers can now analyze circuits with equations, rather than antiquated state diagrams."Sounds like jolly fun for somebody else----for academics who have to publish and never have to make things that work. For example, the standard definition of m to the n power is m times itself n times. "This is not only wrong, but it makes us think that taking something to the zeroth power is some kind of mystery," says Spencer-Brown.Well, what's wrong for you may be right for me. I sure hope so.

I sent away for the book, The Laws of Form,5 just to satisfy my curiosity. Maybe it could help me design a better op amp. But when I got it, I found that it has nothing directly related to electronics, or ICs. It shows the philosophy of a certain type of abstract symbolic logic. The book is crammed full of statements such as:

"Distinction is perfect continence." "There can be no distinction without motive, and there can be no motive unless contents are seen to differ in value." "The form of any finite cardinal number of crosses can be taken as the form of an expression." "Knowledge: Let a state distinguished by the distinction be marked with a mark ˥ of distinction. Let the state be known by the mark. Call the state the marked state." "Form: Call the space cloven by any distinction, together with the entire content of the space, the form of the distinction. Call the form of the first distinction the form." "Value: Call a state indicated by an expression the value of the expression."  "Equivalence: Call expressions of the same value equivalent. Let a sign  =  of equivalence be written between equivalent expressions. Now, by axiom 1, ˥  ˥  = ˥ . Call this the form of condensation...."6     

If you like these, then you'll have a lot of fun. And if you want to learn how to make a better flip-flop----well, maybe this book will tell you how to do it. Good luck.

All for now. / Comments invited!  RAP / Robert A. Pease / Engineer


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1. E.E. Times, CMP Publications Inc., 600 Community Dr., Manhasset, NY 11030. Feb. 14, 1994, pp. 1, 31-35; Feb. 21, pp. 31-33.; March 7, pp. 43, 62; March 14, pp. 37-39.

2. E.E. Times, Feb. 14, p. 31, 35.

3. Ibid., p. 34.

4. E.E. Times, March 7, p. 43.

5. The Laws of Form, by George Spencer Brown, Tarati Press, Published by Cognizers Connection, 4th Printing, 1994. Order from Bookmasters, (800) 247-6553 or (419) 281-1802; fax (419) 281-6883. About $50.00, plus $5.00 S&H

6.  Ibid., pp. 1-16.