Simple methods for the calculation of root of a reconfigurable binary tree structure

In a reconfigurable binary tree structure controlled by a shift register with variable bias (SRVB), the root of a particular configuration is a function of the bias applied to the structure. This letter proves two new theorems for the derivation of formulas for the calculation of the root for a given bias. These are simpler than those obtained by Kartashev and Kartashev [1]. Consequently, both the software and hardware implementations are achieved in minimal time and hardware. The letter also presents these implementations in the form of a program and two circuits, one acting as a serial, and the other as a parallel, bias-to-root converter.