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A "trivial" (easy to understand but not practical) conversion function

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• A trivial conversion method to convert string numbers to its 2's complement code
  • You can convert a number string into its 2's complement binary number by testing every possible string input as follows:

    /* --------------------------------------------------------------- Trivial conversion: match the input string to every possible number string and return the corresponding 2's complement binary number --------------------------------------------------------------- */ public static int parseInt( String s ) { if ( s.equals("0") ) return 0; // The return statement will return the binary number // 00000000000000000000000000000000 !! else if ( s.equals("1") ) return 1; // returns: 00000000000000000000000000000001 else if ( s.equals("2") ) return 2; // returns: 00000000000000000000000000000010 ... else if ( s.equals("10") ) return 10; // returns: 00000000000000000000000000001010 else if ( s.equals("11") ) return 11; // returns: 00000000000000000000000000001011 ... else if ( s.equals("-1") ) return -1; // returns: 11111111111111111111111111111111 else if ( s.equals("-2") ) 1eturn -2; // returns: 11111111111111111111111111111110 ... }

  • This method is not practical because you will need to write 2³² (= 4294967296) different cases with the if-statements !!!

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  • Similarly, you can write a naive conversion method that convert a 2's complement binary number into its corresponding number string by testing every possible binary number as follows:

    public static String toString( int x ) { if ( x == 0 ) return "0"; // Returns the ASCII representation for 0 !! else if ( x == 1 ) return "1"; else if ( x == 2 ) return "2"; ... else if ( x == 10 ) return "10"; else if ( x == 11 ) return "11"; ... else if ( x == -1 ) return "-1"; else if ( x == -2 ) return "-2"; ... }

  • This method is also not practical because you will need to write 2³² (= 4294967296) different cases with the if-statements !!!

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• Dictatical comment
  • I want to pause a bit and make sure that you know that:

    When you write this statement in Java: return 5; // Or some other decimal number The Java compiler will generate computer instructions that will: return 5 as a 2's complement binary number, i.e.: 00000000000000000000000000000101        When we write this statement in Java: return "12"; // Or some other string The Java compiler will generate computer instructions that will: return the ASCII code binary numbers   001100001 00110010   (which represents the characters 1 and 2, i.e., the string "12")

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• Prelude to discussing the conversion algorithms
  • This trivial solution will help you understand what the parseInt( ) and toString( ) methods need to do

    But the trivial solutions are not practical because it's impossible to write out 2³² different cases !!!!

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  • We will develop a practical algorithm to perform the conversions !!!!

    But before I can do so, I will present the necessary pre-requisite in character/string manipulation operations of Java (that you have had in CS170/CS171) -- i.e.: refresher)