Cascade squarer

A novel squarer is described in which the required result is a linear combination of readily produced secondary variables. The square of a variable can be expanded in a series, where each term is derived from the preceding one by linear operations and the operations of maximum and minimum selection. `A converted¿ variable is associated with each term of the expansion. The square is equal to a linear combination of the converted variables and the square of the last converted variable. The range of variation of successive converted variables decreases by half, and the series converges by a factor of one quarter per term. The expansion stands in direct correspondence to electronic squaring circuits which use linear elements and diode selection circuits in a cascade connection. When used in conjunction with any half squarer, the cascade squarer increases its accuracy by factors of 4, 16 ¿ if 1, 2 ¿ stages are used. Alternatively, a sufficient number of stages provides a complete squarer. Accuracies of ±0.1% are readily obtained in very simple circuits, and the speed of response is extremely fast. Several examples of circuits of cascade squarers are given.