Negative Base

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A negative base (or negative radix) may be used to construct a non-standard positional numeral system. Like other place-value systems, each position holds multiples of the appropriate power of the system's base; but that base is negative-that is to say, the base scriptstyle b is equal to scriptstyle -r for some natural number scriptstyle r (r ¿ 2). Negative-base systems can accommodate all the same numbers as standard place-value systems, but both positive and negative numbers are represented without the use of a minus sign (or, in computer representation, a sign bit); this advantage is countered by an increased complexity of arithmetic operations. The need to store the "information" normally contained by a negative sign often results in a negative-base number being one digit longer than its positive-base equivalent.