---

Converting a TWO-digits decimal integer string to 2's complement representation

---

• The value of a decimal number
  • Recall from high school:

    Value of the decimal number 12 is computed as: 1×101 + 2×100 = 1×10 + 2×1

    Notice that if we perform the same computation with binary numbers, we will get the binary representation for the same number:

    00000001×00001010 + 00000010×00000001 = 00001010 + 00000010 = 00001100 And: Binary number 00001100(2) is the decimal number 12(10) !!!

    We can use this high school formula and binary arithmetical operations to compute the 2's complement representation from it's string !

  ---

  ---

  ---

  ---

• Example to help you understand the conversion algorithm: convert a number string of 2 characters to 2's complement
  • Before we discuss the algorithm, let's look at how you would convert the string "12" into its 2's complement representation

  • The string "12" consists of 2 ASCII codes 00110001 (= 49) 00110010 (= 50):

       12
    their binary ASCII code:
       0100100001100101011100100110010100100000011000100110010100100000011100110110010101100011011100100110010101110100001000000110110101100101011100110111001101100001011001110110010101110011001000010010000100110001

    Made by @mathias ---- GitHub! source

  • We can individually map the ASCII codes to their 2's complement values that are suitable for binary arithmetic by the mapping function that we found previously:

    "12" consists of the ASCII code: 00110001 00110010 Map each ASCII code uisng "input - 48": 00110001 (=49) - 00110000 (=48) --> 00000001 (=1) 00110010 (=50) - 00110000 (=48) --> 00000010 (=2)

    After we got their computable 2's complement codes for the digits, we can use the high school formula to find the value:

    1×10 + 2 The computer can perform this calculation in binary: 00000001×00001010 + 00000010 = 00001010 + 00000010 = 00001100

    and obtain the 2's complement representation 00001100 for the String "12" !!!

    ---

    ---

  • I made a simple Java program to show you the steps to convert the string "12" to it's 2's complement code 00001100:

    // File: /home/cs255001/demo/atoi/Atoi_1.java // // Convert "12" to 2's complement // public class Atoi_1 { public static void main(String[] args) throws Exception { String s = "12"; // You can use any string of 2 digits int[] v = new int[2]; // To save values of the digits int i; System.out.println("ASCII codes (in decimal) = " + (int) s.charAt(0) + " " + (int) s.charAt(1) ); /* ------------------------------------------------------- Convert the ASCII character to 2's compl - per digit ------------------------------------------------------- */ v[0] = (int) s.charAt(0) - 48; v[1] = (int) s.charAt(1) - 48; i = v[0]*10 + v[1]; // High school formula to find value of dec number // Note: calculation performed in BINARY by computer !!! System.out.println("integer value i = " + i); /* ============================================================= Prive to students that this is an integer (you can add !) ============================================================= */ i = i + 1; System.out.println("After i+1, i = " + i); } }

    Sample output:

    cheung@aruba> java Atoi_1 ASCII codes (in decimal) = 49 50 integer value i = 12 After i+1, i = 13

    Notice that the string "12" is represented by the 2 ASCII codes 00110001 (= 49) 00110010 (= 50) as shown in the sample output.

    When we subtract 48 from them, we get 1 and 2.

    That's why the high school formula can be used to compute the 2's complement representation because 1 and 2 are suitabel for computation (while 49 and 50 are not !!)

    ---

  • Example Program: (Demo above code)                                                
    • Prog file: /home/cs255001/demo/atoi/Atoi_1.java

    How to run the program:

    To compile:   javac Atoi_1.java          To run: java Atoi_1