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Numerical order in signed-digit notation

As in the previous chapter, we order numerals lexicographically. If 64#64 are binary numerals without negative digits, then

65#65 implies 66#66.
This property fails for signed-digit numerals (for example, for 67#67 and 68#68 one has 57#57 but 69#69). Moreover, its converse fails for both standard and signed-digit numerals (for example, for 70#70 and 71#71 one has that 72#72 but 73#73). However, it turns out that signed-digit numerals admit a very strong order-normalization property that standard numerals don't [28].



 

Martin Escardo
2000-10-02