Chapter 4: Systems Based on Numbers

Section 2: Elementary Arithmetic

Negative bases

Given a suitable list of digits from 0 to k - 1 one can obtain any positive or negative number using FromDigits[list, -k]. The picture below shows the digit sequences of successive numbers in base -2; the row j from the bottom turns out to consist of alternating black and white blocks of length 2j. (In ordinary base 2 a number -n can be represented as on a typical electronic computer by complementing each digit, including leading 0's.) (See also page 1093.)

Image Source Notebooks:

From Stephen Wolfram: A New Kind of Science [citation]