Improvement of Radix-2 Signed-Digit Number for High Speed Circuit

In this article, a new radix-2 signed-digit number (Radix-2 sub signed-digit number) is defined and its properties for hardware realization are discussed. Until now, high speed calculation method with Radix-2 signed-digit numbers is proposed, but this method used “Compares With 2” to calculate carry. “Compares with 2” is a very simple method, but it needs very complicated hardware especially when the value of k becomes large. In this article, we propose a subset of Radix-2 signed-digit, named Radix-2 sub signed-digit numbers. Radix-2 sub signed-digit was designed so that the carry calculation use “bit compare” to hardware-realization simplifies more. In the first section of this article, we defined the concept of Radix-2 sub signed-digit numbers and proved some of their properties. In the second section, we defined the new carry calculation method in consideration of hardwarerealization, and proved some of their properties. In the third section, we provide some functions for generating Radix-2 sub signed-digit numbers from Radix-2 signed-digit numbers. In the last section, we defined some functions for generation natural numbers from Radix-2 sub signed-digit, and we clarified its correctness.