Negative-Base Number-Representation Systems

Number-representation systems employing negative bases, and identical in structure to the usual systems using positive bases, can represent both positive and negative numbers with equal facility. Arithmetic involving both positive and negative operands can also be performed in a negative-base system without special attention to the negative numbers. Determination of whether a number is positive or negative is relatively difficult, such determination depending upon knowledge of the position of the most significant digit. Truncation and roundoff errors in negative-base systems are greater relative to positive-base systems. An algorithm for representing numbers in a system with a negative integral base is given, and rules for common arithmetic operations are presented.