#include #include #include #include /* Converts a fraction like 0.5 or 0.275 to an arbitrary base * 0.010100101 ...base 2 * 0.abc ...base 16 * * Reverses it to confirm how many symbols are significant * * Any decimal number can be converted to another base by: Multiply fraction by # of symbols representing the base Extracting integer (or 0) Translate that integer to the correct symbol Repeat until everything to the right of the dot is zero */ const int TARGET_BASE_INDEX = 4; // select from targetBases[] const float FRACTION = 0.21745f; // what to convert // No nulls. First char represents 0; last is max. std::string targetBases[] = { "0123456789abcdef", // hexadecimal "0123456789", // decimal (test) "01234567", // octal "01", // binary "abcdefghijklmnopqrstuvwxyz", // base 26 // base 60 "0123456789abcdefghijklmnopqrstuvwxyz!@#$%^&*()-_=+<>[]{}/?,;" }; // returns how many symbols were generated int getSymbols(float candidate, char buf[], int buflen, char* base) { float workvar; workvar = candidate - trunc(candidate); // discard integer portion int intBase = std::strlen(base); // what base are we seeking? std::cout << "Base " << intBase << std::endl; int symbolPosition = 0; while(symbolPosition < (buflen-1)) { workvar *= (float)intBase; int tmp = trunc(workvar); buf[symbolPosition] = base[tmp]; symbolPosition++; workvar -= tmp; if(workvar == 0.0f) { buf[symbolPosition] = 0; break; } } return symbolPosition; } // What float value is the new-base fraction? float crossCheck(char buf[], char* base, float targetVal) { float fsum = 0.0f; int i = 1; int intBase = std::strlen(base); while(buf[i-1] != 0) { // null float bitset = (buf[i-1] != base[0]); // is there a 1 here? if(bitset) { // find the offset; that's the multiplier char* where = std::strchr(base, buf[i-1]); int multiplier = where-base; fsum += multiplier * pow(intBase, -i); // add multiplier/(base^i) } std::cout << i << ": " << fsum; if(fsum == targetVal) { std::cout << " ** MATCH at " << i << " symbols." << std::endl; return fsum; } std::cout << std::endl; i++; } return fsum; } char buf[500]; int main() { // Display original fraction std::cout << " Original: " << FRACTION << std::endl; char* targetBase = &targetBases[TARGET_BASE_INDEX][0]; // Calculate binary fraction, then display it int symbolsInAnswer = getSymbols(FRACTION, buf, 500, targetBase); std::cout << " " << symbolsInAnswer << " symbol(s): " << targetBase[0] << "." << buf << std::endl; // Reverse value to float again float check = crossCheck(buf, targetBase, FRACTION); if(FRACTION == check) { std::cout << "--> Success!" << std::endl; return 0; } else { std::cout.precision(17); std::cout << "--> Mismatch by: " << std::fixed << check-FRACTION << " :("; return 1; } return 0; }

decimal fraction -> any base (2 to 255)