Combinational and Sequential Cellular Structures

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Abstract
Cellular arrays composed of identical cells with uniform interconnections are presented. The basic cell is a switching device with two inputs, two outputs, and two control variables x and T. The cell structure is either purely combinational or with unit delay depending upon the control variable T. The control variable x sets up either a ``crossing mode'' or a ``bending mode'' in the cell. Thus a two-dimensional cellular array without time delays has the connection capabilities of a crossbar switch. Any combinational switching function can be realized by appropriate choice of control variables while the inputs to the edges of the plane are fixed. Alternatively, the control variables can be fixed while the inputs to the edges of the cellular plane are varied from function to function. A cubic array is constructed from a set of identical cellular planes packed one upon the other such that the control variables applied to the first plane will penetrate to all other planes without time delay. It is shown that any k functions of the same variables can be synthesized on such a cubic array. By allowing the control variable T to delay some signals in the array, such a cubic array can be used to realize any synchronous sequential machine with single or multiple inputs and/or feedback functions. Any defective cell in the array can be tested and isolated. The array can be stripped, divided, or interconnected.

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