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Converting a 2's complement representation to it's ASCII string representation

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• Sketch of the ASCII representation -> 2's complement representation conversion algorithm
  • The following diagram illustrates the steps to convert a number given in the 2's complement representation and convert it to an equivalent ASCII representation using a concrete example (12):

    Input: 12 2's complement representation is: 00000000000000000000000000001100 (1) Divide the input repeatedly by 10 and collect the remainder of the division. This step will generate the individual decimal digits as follows: 12 ÷ 10 = 1 with remainder 2 repeat: 1 ÷ 10 = 0 with remainder 1 done (2) Map each digit remainder to the corresponding ASCII code with: ASCII code = digit + 48 This step will generate the ASCII codes: 50 ('2') 49 ('1') (3) Concatenate the ASCII codes into a string starting from the last remainder to the first remainder

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  • Caveat:

    We must take care of the negative integers !!!

    If the integer value is negative (< 0), we must:

    Negate the integer (= flip the bits and add 1) Now the integer is positive !!! We can perform the conversion (on the now positive value) using the above algorithm To finalize the string, we just prepend the dash character '-'

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  • The complete conversion algorithm is as follows:

    Input: (sample) -12 2's complement representation is: 11111111111111111111111111110100 (0) If ( input < 0 ) { Remember that input is negative; input = -input; // This is the 2's compl negate operation // Input is now: 00000000000000000000000000001100 (=12) } (1) Divide the input repeatedly by 10 and collect the remainder of the division. This step will generate the individual decimal digits as follows: 12 �� 10 = 1 with remainder 2 repeat: 1 �� 10 = 0 with remainder 1 done (2) Map each digit remainder to the corresponding ASCII code with: ASCII code = digit + 48 This step will generate the ASCII codes: 50 ('2') 49 ('1') (3) Concatenate the ASCII codes into a string starting from the last remainder to the first remainder (4) If ( input was negative ) { prepend the character '-' to the output; }

    The algorithm expressed in Java is as follows:

    /* --- myToString(): Integer to Ascii conversion function --- */ public static String myToString(int input) { boolean inputWasNeg; int remainder[] = new int[100]; char digit[] = new char[100]; // Max 100 digits in number String result; int nDigits; /* --------------------------------------- Check if input is negative --------------------------------------- */ if (input < 0) { inputWasNeg = true; input = -input; // Negate to make input positive } else { inputWasNeg = false; } /* ------------------------------------------------------- Get all digit by collecting remainders divided by 10 ------------------------------------------------------- */ nDigits = 0; // Count # digits in number while (input > 0) { remainder[nDigits] = input % 10; nDigits++; input = input / 10; } /* --------------------------------------------------------- Convert "digits" to character (ASCII code) using: ASCII code = digit + 48 --------------------------------------------------------- */ for (int i = 0; i < nDigits; i++) { digit[i] = (char) (remainder[i] + 48); // Or use '0' for 48 } /* --------------------------------------------------------- Make a string (start with last remainder) --------------------------------------------------------- */ result = ""; // Initialize output string for (int i = nDigits-1; i >= 0; i--) result = result + digit[i]; // Add next digit /* --------------------------------------------------------- Prepend '-' if input was negative --------------------------------------------------------- */ if ( inputWasNeg == true ) { result = "-" + result; // Try: "******" + result for banks } else { result = result; // Does nothing... } return(result); }

    The algorithm is doing exactly what I describe with the example...

    (1) In the "Check if input is negative" code segment we test input < 0 If so: we set inputWasNeg = true and negate the input If not: we set inputWasNeg = false (2) In the "Get all digit by collecting remainders divided by 10" we divide the input repeatedly by 10 The remainders of the division are stored in: reminder[0] reminder[1] .... remainder[nDigits-1] (3) In the Convert "digits" to character (ASCII code) we convert each reminder[i] to its digits using: digit[i] = remainder[i] + 48 (4) In the Make a string (start with last remainder) we make this string: "digit[nDigits-1] digit[..] .... digit[1] digit[0]" (5) Finally, in the input was negative, we prepent a '-' character to the result.

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  • Example Program: (Demo above code)                                                

    How to run the program:

    get a copy of the program at: /home/cs255001/demo/atoi/Itoa.java To compile:   javac Itoa.java To run:          java Itoa