# Computers will be more than 1s & 0s

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Over the last 40 years work in Maryland's Microsystems Laboratory has been directed toward developing hardware for new classes of computers. The classes can be broken into four basic types: number based, group theory based, wave based and biologically based.

The standard computer of today is normally called a "Von Neumann type" and its hardware is designed for models associated with the binary number system-that, is numbers represented by strings of logical 0 or 1 values.

Essentially, these computers use logic based upon the group property under addition of polynomials in powers of two with coefficients that are binary. Some other operations are included, such as overflows and carries. These computers have the beautiful property of being realized with CMOS circuits using combinations of a single gate, the NAND gate. Their commercial viability lies in the fact that CMOS transistors can be economically fabricated in extremely large numbers (on the order of millions) via VLSI processes on small chips.

Nevertheless, these Von Neumann computers do have some limitations, such as difficulties in handling defects in the chip or handling simultaneously multiple signals.

Rather than using powers of two for the number base there is some advantage in using the Fibonacci numbers, those that are the sum of the previous two in the sequence, thus, 1, 1, 2, 3, 5, 8, etc., rather than the 1, 2, 4, 8, 16. . . sequence of binary powers. Although slightly less efficient, these Fibonacci numbers have the advantage that any one of them can be deleted with the remaining ones still forming a complete set. This means that one does not need to do a separate coding to take care of a fault since the fault can be absorbed in the number system itself.

One can use binary numbers as coefficients on the Fibonacci numbers, in which case the standard CMOS NAND gates serve to give suitable hardware for the resulting computers, which we have called Fibonacci computers. But one can conveniently use ternary numbers, (-1, 0, +1), as coefficients in monomials in the Fibonacci numbers to give more convenient hardware realizations. In effect, -1 goes with a negative bias voltage, +1 with the positive bias and 0 with ground potential.

Stranger to engineers is another number system that offers some advantages in that it gives exact results for large numbers of rational numbers; this is the p-Adic number system. It is based in essence upon infinite series in a prime p with positive and negative powers rather than the polynomial bases of Von Neumann computers.

Since in essence the computers, as we are familiar with them, carry out the operations of a group as technically defined by the mathematicians and since every group has a representation as a permutation group, there is some interest in making hardware to realize permutation groups.

Since permutations are just interchanges, hardware realizations need only be interchanges of wires, which leads to very simple standard cells from which all logic can be constructed. These cells can be made universal by concentrating on the somewhat all-inclusive symmetric groups using CMOS transistors to configure the interchanges in real-time, making for very flexible designs of computers.

In the group theory category we also have studied the use of elliptic curves with a thesis that is ongoing for hardware construction. Here a branch of an elliptic curve is realized by a set of CMOS transistors, each of which gives a quadratic, in cascade with cancellation of the quartic terms to yield the cubic as a remainder. Then to obtain the group law a load line is passed through the cubic with variable slope to yield the group addition for different real numbers. The load lines are again realized in standard ways by CMOS transistors with variable gate voltages to adjust the slope.

Some of the Microsystems Laboratory's more fascinating studies in the computer area have been associated with the soliton computer. These computers have the very useful property of being able to process more than one set of data truly simultaneously, not through multiplexing as used on a single Von Neumann computer. The idea is based upon that of water waves, called solitons in the mathematical and fluid dynamics literature, generated by throwing a rock in a pond-throw two rocks and the wave resulting from the harder thrown one will travel undisturbed through a previously generated wave from a more softly tossed rock. Analogies of the water waves are realized by CMOS circuits and allow for the same transistors to be simultaneously working on several soliton waves.

This calls for rather tricky circuit design and leads to good theoretical studies for university work. But because the waves need space in which to travel their practicality still seems to be in the future.

However, microfluidic computers should prove of considerable practical interest since in the last decade microelectromechanical (MEM) devices, with moving parts the size of transistors, have become quite practical. Here we can construct NAND gates by cross-directing one fluid onto another. The fluid flows in etched channels and can be powered by micromotors. One advantage appears to be that these microfluidic computers could work at temperatures where transistor-based circuits cease to operate.

Finally, we should mention the biologically based computers. Our interests in these started in the 1960s with the neuristor. With the advent of the biologically based but very efficient DOS program Synetsim we were able to make circuits realizing the various modules of that program while replacing table lookup with our neural-type cell, which is an adaptation of the neuristor. In particular the Hartline pools, which are the key elements in neural behavior of these systems, now have nice CMOS circuit realizations.

Besides these neural-type circuits, others have been developed in the laboratory, some of which are associated with more recent systems known in a rather extensive literature as neural networks. Some of these neural networks have proved to be of value in carrying out functions for which there are only vague mathematics available.

**Wings and ears**

However, much more can be done. For example, a system for control of insect wings has been developed in the laboratory that appears applicable to the control of microair vehicles for which a neurally inspired guidance system based upon optical flow has been developed. We also are developing neural networks to control our ear-type systems.

Even more fascinating is the use of live neurons on a silicon chip. Various laboratories around the world are looking at this possibility but so far the major problem we have faced is that of keeping neurons alive for more than a week or two. In any event, neurons can be made to grow synapses on a chip so that they become patterned for desired connections.

Since chips with real neurons growing on them should prove extremely valuable as chemical sensors, we are interested in designing chips on which neurons can be tuned to different classes of chemicals, especially toxic ones.

Related to that is the possibility of patterning various proteins to behave in desirable ways. Since DNA has an interesting connectivity structure, we wish to apply n-port circuit synthesis techniques to the design of specified structures. Clearly, interacting CMOS transistor and circuit theoretical technology with live biological neural capabilities can open areas for study within several fields.

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