Binarysigneddigitrepresentation(BSD-R)ofanintegeriswidelyusedincomputerarithmetic,cryptographyanddigitalsignalprocessing.ThispaperstudieswhattheexactnumberofoptimalBSD-Rofanintegerisandhowtogeneratethementirely.WealsoshowwhichkindsofintegershavethemaximumnumberofoptimalBSD-Rs.