Editing Signed-digit representation (section)

==Other systems==
There exist other signed-digit bases such that the base <math>b \neq b_{+} + b_{-} + 1</math>. A notable examples of this is [[Booth encoding]], which has a digit set <math>\mathcal{D} = \lbrace\bar{1},0,1\rbrace</math> with <math>b_{+} = 1</math> and <math>b_{-} = 1</math>, but which uses a base <math>b = 2 < 3 = b_{+} + b_{-}  + 1</math>. The standard [[binary numeral system]] would only use digits of value <math>\lbrace0,1\rbrace</math>.

Note that non-standard signed-digit representations are not unique.  For instance:

: <math>0111_{\mathcal{D}} = 4 + 2 + 1 = 7</math>
: <math>10\bar{1}1_{\mathcal{D}} = 8 - 2 + 1 = 7</math>
: <math>1\bar{1}11_{\mathcal{D}} = 8 - 4 + 2 + 1 = 7</math>
: <math>100\bar{1}_{\mathcal{D}} = 8 - 1 = 7</math>

The [[non-adjacent form]] (NAF) of Booth encoding does guarantee a unique representation for every integer value. However, this only applies for integer values. For example, consider the following [[Repeating decimal#Extension to other bases|repeating binary]] numbers in NAF,
: <math>\frac{2}{3} = 0.\overline{10}_{\mathcal{D}} = 1.\overline{0\bar{1}}_{\mathcal{D}}</math>