A computing technique is described which employs several computing elements to solve algebraic, transcendental and integro-differential equations operational-digital. Information between the different computing elements is carried in the form of pulse-width signals. Each computing elements employs only digital circuits, but in an analog fashion. The proposed hybrid technique overcomes the accuracy limitations of the conventional analog technique and the analog-digital interface problems of the various digital techniques, while it retains many of the advantages of both the analog and the digital technique. In general, hybrid operational computing elements are insensitive to environmental, component tolerances and power supply changes, have small size, small weight and minimum power consumption (only one supply voltage required) and can be instrumented with 100 per cent integrated circuits. Although the proposed hybrid technique has no basic accuracy limitation it will operate most economically with accuracies below one part in 105. Similarly, it is not practical to operate with repetition frequencies in excess of 10 kc. Maximum accuracy can be had only at very low repetition rates, while maximum speed can be had only at very low accuracy, since the product of repetition rate and accuracy is a constant for a certain quality of digital circuits. Finally, the inherent storage capability and the ease with which pulse-width signals can be switched facilitates sequential operation of hybrid operational computing elements. Therefore, cost, size and weight can be drastically reduced if bandwidth can be sacrificed.

A single-variable function generator, based on a pulse averaging method,1 accepts a width-modulated pulse input. The clock generator accuracy determines the precision with which this device can produce a linear-segment curve. With 300-kc flip-flops in the clock, a static repeatability of ±0.02 per cent has been obtained with a carrier frequency of 100 cps, and ±1 per cent with a 10-kc carrier frequency. This device can multiply the single-variable function by a second input variable at no loss of accuracy and with no additional circuitry.

This article describes a four-quadrant time-division multiplier with an over-all accuracy of better than 0.1 per cent of full scale. The circuit is independent of the transistor characteristics, requires no complicated balancing adjustments, exhibits excellent stability and uses only simple, noncritical circuitry. The maximum output voltage is 10 v when both input voltages are 10 v.