B.S.T.J. Briefs: Extension of Multidimensional Polynomial Algebra to Domain Circuits With Multiple Propagation Velocities

Multidimensional Polynomial Algebra 1 is a new technique for the analysis of circuits in which a finite and distinct time interval is necessary for the propagation of binary bits of data from one location to the next. These conditions exist specifically in magnetic domain circuits. 2,3 The algebra expands the basic concepts of the coding theorists, 4,8 and includes the representation of both time and space in the algebraic representation of data streams. A set of algebraic transformations 1 has been developed to correspond to the subfunctions in the circuit, and the overall function is thus modeled by a series of algebraic transformations. Such an analysis predicts the location and the value of all the binary positions at any prcchosen instant of time, thus leading to the algebraic verification of the operation of a proposed circuit. In the foregoing technique for analysis, one velocity of propagation was assumed. However, the circuit designer may depend on more than one velocity for the successful operation of the circuit, and the technique suggested here accounts for different propagation velocities. Further, the analysis proposed determines the relationships between such velocities. In discrete circuits, multiple velocities are generally derived from clock sources driven at different rates. The movement from one location to the adjoining location is finite, but the duration for the movement is derived from different clocks.