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Introduction: converting ASCII representation of numbers to 2's complement representation and vice versa

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• Review of the ASCII representation and the 2's complement representation of integer value (whole number)

  • Recall that computers use the 2's complement code to represent (signed) integer (number) values used for computation:

    value Representation in 8 bits Repr in 16 bits --------+----------------------------+-------------------- ... ... .... -3 11111101 1111111111111101 -2 11111110 1111111111111110 -1 11111111 1111111111111111 0 00000000 0000000000000000 1 00000001 0000000000000001 2 00000010 0000000000000010 3 00000011 0000000000000011 ... ... ....

    The computer can easily perform +, -, *, / operations on integer values when they are in 2's complement code

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  • Recall also that the key board/terminal that humans use to input/output numbers use:

    ASCII code

    Examples:

    Number (String) Representation ------------------+---------------------- "1" 00110001 "12" 00110001 00110010

    (These are sometimes call "numerical strings")

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  • Therefore, before the computer can perform computation on the integer numbers entered in the key board, it must convert the ASCII representation into 2's complement representation.

  • Furthermore, in order to display a number in 2's complement representation on a terminal, we must convert the 2's complement representation into ASCII representation first !!!

    (Because a terminal can only display characters according to their ASCII codes).

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• Converting (translating) between the 2 number representations
  • In the next few webpages in the CS255 syllabus, we will study how to convert between ASCII representation (of numbers) and 2's complement represention (of the same number).

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  • BTW: the Java standard library has provides conversion methods between ASCII <--> 2's complement representations inside the Integer class to the Java programmers:

    int parseInt( String s ): return the int value translated from the input string s String toString( int x ): return a String that represents the integral value x

    So basically we will be studying how these methods are written.

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  • In CS170, you learned how to use those methods to convert between String (= ASCII representation) and int (= 2's complement representation):

    String s = "-123"; int i; i = Integer.parseInt( s ); // Convert number string into integer s = Integer.toString( i ); // Convert integer value to string

    Here in CS255, I will show you what happens inside these 2 conversion methods

    I.e.: I will show you the algorithm used inside the Java conversion methods.

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• Making sure you understand what exactly is the problem
  • There are 2 problems that we are solving:

    An input problem: A signed number used in computation is represented using the 2's complement code inside the computer However: the user can only enter a signed number on the key board that transmit ASCII codes to the computer The Integer.parseInt( String ) method solves the input problem by converting an ASCII representation of a number into its 2'c complement code Examples of Integer.parseInt( ) results: Integer.parseInt( "1" ) returns 1 (= 00000000000000000000000000000001) Integer.parseInt( "-1" ) returns -1 (= 11111111111111111111111111111111) Note: I want to make sure that you know that "1" is this sequence of ASCII code: 00110001 "-1" is this sequence of ASCII code: 00101101 00110001 (00101101 is code for the '-' char) An output problem: A signed number used in computation is (as before) represented using the 2's complement code inside the computer However: the computer can only display a signed number as (a sequence of) characters by transmiting ASCII codes of the digits to the terminal The Integer.toString( integer ) method solves the output problem by converting a 2's complement representation of a number into its (sequence of) character ASCII codes Examples of Integer.toString( ) results: Integer.toString( 1 (= 00000000000000000000000000000001) ) returns "1" Integer.toString( -1 (= 11111111111111111111111111111111) ) returns "-1" Note: see note above on what "1" and "-1" means A string inside the computer is actually an array (= sequence) of character (codes) !!!