The negabinary representation of a number n is given by the coefficients in

where . Conversion of n to negabinary can be done using the Mathematica code

Negabinary[n_Integer] := 
  Module[{t = (2/3)(4^Floor[Log[4, Abs[n] + 1] + 2] - 1)}, 
    IntegerDigits[BitXor[n + t, t], 2]] 

due to D. Librik (Szudzik). The bitwise XOR portion is originally due to Schroeppel (1972), who noted that the sequence of bits in n is given by .

The following table gives the negabinary representations for the first few integers (A039724).

If these numbers are interpreted as binary numbers and converted to decimal, their values are 1, 6, 7, 4, 5, 26, 27, 24, 25, 30, 31, 28, 29, 18, 19, 16, ... (Sloane's A005351). The numbers having the same representation in binary and negabinary are members of the Moser-de Bruijn sequence, 0, 1, 4, 5, 16, 17, 20, 21, 64, 65, 68, 69, 80, 81, ... (Sloane's A000695).

 

Binary, Moser-de Bruijn Sequence, Negadecimal