# The Fred and Ann Approach

The main reason that we are developing a trinary logic system is that it has the potential of being immensely useful in computers (see the uses page for elaboration on this). And, for it to be useful we need to be able to do math with our logic system. Thus we need to be able to build a half adder with our system.

We have had lots of problems developing a half adder using the notation of the Bob, Ike and Qui system (there is serious doubt as to whether or not it is even possible), so we decided to try out a new notation for our gates. Here's an explanation of this wonderous new notation for trinary gates...

# The Notation

The box gates in the Bob, Ike and Qui system are somewhat restricting. There are certain combinations of inputs and outputs that simply cannot be achieved using that type of notation for the gates. So, instead of using boxes, we found that grids work much better. Here is an example of a gate written with this new notation:

Each column represents one possible input, and each row represents the other. The cell at the intersection of any given column and row contains the output for that combination of inputs. Under this notation, any combination of inputs and outputs is possible.

Once we began to use this notation, assembling a half adder was simple. We made two gates for this purpose: Fred and Ann.

 p q sum carry 2 2 1 1 2 1 0 1 2 0 2 0 1 2 0 1 1 1 2 0 1 0 1 0 0 2 2 0 0 1 1 0 0 0 0 0
Looking at the truth table for the trinary half adder, you may notice that the Ann's outputs correspond to the sum column of the truth table, and Fred's outputs correspond to the carry column. Thus, a half adder using Fred and Ann would look like this:

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# The Drawbacks

As wonderful as this half adder may seem, it does have one major drawback. Because the design of the gates is somewhat arbitrary, we are not sure how possible it would be to actually build a logic gate like Fred or Ann for use in a computer. In the notation of Bob, Ike and Qui, all outputs are at the end of a distinct line which could also be a parallel to the flow (or lack thereof) of electricity through the gate. But with the grid notation it is not always possible to draw lines to represent the connection between inputs and outputs (ironically, that was our major reason for adopting this notation), so it may not be physically possible to build a gate such as Fred or Ann. But, until one of us learns the details of chip design, the jury remains out on this one. The grid notation may be the answer to all of our problems, or it may just be a dead end. We shall just have to wait and see...

Well, now you know all of the possibilities that we have found so far for the creation of a trinary logic system. But you're probably asking yourself, "So what??!!!" Well, click here to find out potential uses for a trinary logic system.