Negaternary

From Free net encyclopedia

Numeral systems List of numeral system topics
Hindu-Arabic system History Symbol sets: Western Arabic Eastern Arabic Indian family Thai Abjad Armenian Babylonian Brahmi Chinese Cyrillic Egyptian Etruscan Ge'ez Greek Attic Ionian Hebrew Japanese Khmer Korean Mayan Roman D'ni (fictitious)
Positional systems with various bases:
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 20, 24, 26, 27, 30, 32, 36, 60, 64 Non-standard systems: 1, -2, -3, Balanced ternary, mixed, Factoradic, Fibonacci coding, bijective, 2i, φ
edit

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.