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Monadic Gates, Take 1

A project log for Tern - Ternary Logic Circuits

A series of ternary logic gates and higher level components implemented in the real world.

Mechanical AdvantageMechanical Advantage 06/15/2015 at 07:290 Comments

The simplest gates are those which only take one input have only one output. Monadic gates are important building blocks to more complex/useful gates, but they can be useful by themselves in some circumstances. In binary there are only 4 of these (2^2 = 4) but in ternary systems there are 27 (3^3 = 27). Much of what I am trying to demonstrate is described in Dr. Douglas W. Jones' description of ternary logic and I use his naming conventions.

Binary monadic gates:

Buffer/Driver

InOut
00
11

Inverter

InOut
01
10

Constant 0 (not really useful, but here for completeness)

InOut
00
10

Constant 1 (not really useful, but here for completeness)

InOut
01
11

Ternary monadic gates

0123456789ABCDEFGHKMNPRTVXZ
--0+-0+-0+-0+-0+-0+-0+-0+-0+
0---000+++---000+++---000+++
+---------000000000+++++++++

(The labels in the top row are names for a series of three trits. Just like hexadecimal is just a naming scheme for series of 4 bits. This system is called heptavintimal - base 27)

The goal is to test the two devices I am using (a Fairchild Semiconductor LM319 dual comparator and a Motorola LM393 dual comparator) and see which monadic operations they can produce. Three of the operations (0, D, and Z) are trivial because they are always -, 0, or +. That is equivalent to just attaching the signal to the appropriate -5V, GND, or +5V rail. That leaves only 24 monadic operations to work out.

The comparators have a - input and a + input. If the + input is greater than the - input then the output line allows current to flow through it to ground. The LM393 allowed me to use both the +5V and the GND lines on the output pin but the LM319 only allowed me to use +5V. That made the LM393 more versatile, but the LM319 handled low signals differently. Low signals on the LM319 returned GND while the LM393 returned -5V for it's low signal. The result is that both devices would produce a subset of the monadic operations, but each was a different subset. Together they took care of 12 possible combinations. Add that to the 3 trivial operations and there are 15 out of 27 monadic operations accounted for using just the power rails, or only a single comparator.

The LM393 can produce the following monadic operations: 1,2,4,8,9,C,K, and V. Diagram

The LM319 can produce the following monadic operations: E,H,R, and X. Diagram

If you look carefully you'll notice the pattern that each monadic operation we can produce is a pattern of 2 outputs that are the same and one that is different. Also, the one that is different is alway the top or bottom one, never the middle. This is a consequence of how a comparator always chooses the greater of two inputs to make it's decision as to whether or not to output. Hopefully, by chaining together the monadic gates now possible I can make the remaining ones.

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