Efficient G⁴FET-Based Logic Circuits

Fewer G⁴FETs than conventional transistors would be needed to implement logic functions.

A total of 81 optimal logic circuits based on four-gate field-effect transistors (G⁴FETs) have been designed to implement all Boolean functions of up to three variables. The purpose of this development was to lend credence to the expectation that logic circuits based on G⁴FETs could be more efficient (in the sense that they could contain fewer transistors), relative to functionally equivalent logic circuits based on conventional transistors.

The theoretical basis of this development was summarized in “G⁴FETs as Universal and Programmable Logic Gates” (npo-41698) NASA Tech Briefs, Vol. 31, No. 7 (July 2007), page 44. To recapitulate: A G⁴FET is a combination of a junction field-effect transistor (JFET) and a metal oxide/ semiconductor field- effect transistor (MOSFET) superimposed in a single silicon island and can therefore be regarded as two transistors sharing the same body. A G⁴FET can also be regarded as a single device having four gates: two side junction- based gates, a top MOS gate, and a back gate activated by biasing of a silicon- on-insulator substrate. Each of these gates can be used to control the conduction characteristics of the transistor; this possibility creates new options for designing analog, radio-frequency, mixed-signal, and digital circuitry. One such option is to design a G⁴FET to function as a three-input NOT-majority gate, which has been shown to be a universal and programmable logic gate. The universality and programmability could be exploited to design logic circuits containing fewer discrete components than are required for conventional transistor-based circuits implementing the same logic functions.

Optimal NOT-majority-gate, G⁴FET-based logic-circuit designs were obtained in a comparative study that also included formulation of functionally equivalent logic circuits based on NOR and NAND gates implemented by use of conventional transistors. [NOT gates (inverters) were also included, as needed, in both the G⁴FET- and the NOR- and NAND-based designs.] In the study, the problem of finding the optimal design for each logic function and each transistor type was solved as an integer- programming optimization problem. The table summarizes results obtained in this study for the first four Boolean functions, showing that in most cases, fewer logic gates are needed in the NOT-majority (G⁴FET) implementation than in the NOR- and NAND-based conventional implementations. Considering all 81 non-equivalent Boolean functions included in the study, it was found that in 63 percent of the cases, fewer logic gates (and, hence, fewer transistors) would be needed in the G⁴FET-based implementations.

This work was done by Farrokh Vatan of Caltech for NASA’s Jet Propulsion Laboratory.

In accordance with Public Law 96-517, the contractor has elected to retain title to this invention. Inquiries concerning rights for its commercial use should be addressed to:
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Refer to NPO-44407, volume and number of this NASA Tech Briefs issue, and the page number.