Negaternary

From Wikipedia, the free encyclopedia

Numeral systems by culture
Hindu-Arabic numerals
Western Arabic Eastern Arabic Khmer	Indian family Brahmi Thai
East Asian numerals
Chinese Japanese	Korean
Alphabetic numerals
Abjad Armenian Cyrillic Ge'ez	Hebrew Ionian/Greek Sanskrit
Other systems
Attic Etruscan Roman	Babylonian Egyptian Mayan
List of numeral system topics
Positional systems by base
Decimal (10)
2, 4, 8, 16, 32, 64, 128
3, 9, 12, 24, 30, 36, 60, more…
v • d • e

Negaternary is a non-standard positional numeral system in which numbers are written as sums of successive powers of -3. The three digits are 0, 1, and 2. The advantage of using a negative radix is that there is no longer a need for a minus sign; negative numbers can be written the same way as positive numbers. (Compare with balanced ternary in which the radix is positive 3 but the digits are -1, 0, and 1.) Here are the integers from negative ten to ten in both decimal and negaternary:

-10  1212
 -9  1200
 -8  1201
 -7  1202
 -6    20
 -5    21
 -4    22
 -3    10
 -2    11
 -1    12
  0     0
  1     1
  2     2
  3   120
  4   121
  5   122
  6   110
  7   111
  8   112
  9   100
 10   101

As in negabinary, negative numbers have an even number of digits, and positive numbers have an odd number of digits.