// decimal_to_base( less than 10).cpp // Date: 05/05/2020 // Author: G.T.T #include #include #include #include // modf, pow const char k_pt { '.' }, k_zero { '0' } ; std::string hand_multiply( const std::string &lhs, const std::string &rhs ); int main() { using std::cout; using std::endl; const std::string s ("684.4704"); // base 10 number std::istringstream is ( s ); double num1 { 0.0 }, integral, fraction; is >> num1; fraction = std::modf( num1, &integral ); std::string res; const std::size_t radix { 5 }; // base to convert to // integral part calculations if ( integral != 0.0 ) { std::size_t rem { static_cast( integral ) % radix }, quotient { static_cast( integral ) / radix }; res += static_cast( k_zero + rem ); while ( quotient ) { rem = quotient % radix; res.insert( 0, 1, static_cast( k_zero + rem ) ); quotient /= radix; } } // fractional part calculations if ( fraction != 0.0 ) { res += k_pt; std::size_t count { 1 }; // to do while ( fraction != 0.0 && count < 2 ) { std::string s1( std::to_string( fraction ) ), s2( std::to_string( radix ) ), s3( hand_multiply( s1, s2 ) ); std::istringstream is( s3 ); is >> num1; fraction = std::modf( num1, &integral ); res += static_cast( k_zero + integral ); } } cout << s << " (base 10) is equivalent to " << res << " (base " << radix << ")"; } std::string hand_multiply( const std::string &lhs, const std::string &rhs ) { using std::string; string s1( lhs ), s2( rhs ); // remove any trailing zeros, calculate pos string::size_type pos, p1 { s1.rfind( k_pt ) }, p2 { s2.rfind( k_pt ) }, none { string::npos }; auto end1( s1.crbegin() ), end2( s2.crbegin() ); if ( p1 != none ) { while ( *end1 == k_zero ) // use lambdas or ???, minimize repeat code { s1.pop_back(); end1 = s1.crbegin(); } pos = s1.substr( p1 + 1 ).size(); } else pos = 0; if ( p2 != none ) { while ( *end2 == k_zero ) { s1.pop_back(); end2 = s2.crbegin(); } pos += s2.substr( p2 + 1 ).size(); } const std::size_t base { 10 }; // Why? std::size_t i { 0 }, sum { 0 }; //const char k_pt { '.' }, k_zero { '0' }; for ( auto iter1( s1.crbegin() ); iter1 != s1.crend(); ++iter1, ++i ) { char c1 { *iter1 }; if ( c1 == k_pt ) { --i; continue; // ignore point } std::size_t digit1 { static_cast( c1 - k_zero ) }, j { 0 }, inner_sum { 0 } ; double num1 { digit1 * pow( base, i ) }; for ( auto iter2( s2.crbegin() ); iter2 != s2.crend(); ++iter2, ++j ) { char c2 { *iter2 }; if ( c2 == k_pt ) { --j; continue; // ignore point } std::size_t digit2 { static_cast( c2 - k_zero ) }; double num2 { digit2 * pow( base, j ) }, product { num1 * num2 }; inner_sum += product; } sum += inner_sum; } string res; res += std::to_string( sum ); if ( pos != 0 ) res.insert( res.size() - pos, 1, k_pt ); return res; } /* Program notes ------------- 1. i updates the place value in s1, j updates place value in s2 2. Separate integral & fractional parts using modf function in cmath 3. Boolean condition is false if count is more than 1 or fraction is 0.0; count monitors any repeat fractions, indication of repeating unending number pattern. 4. Line 87. Why must base used be 10? This requires a mathematical explanation. Base to convert to only passed as rhs string. */

Revised: decimal_to_base( less than 10 )