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Converting between the integer datatypes (int, short, and byte)

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• Converting between 2s complement codes of different lengths
  Quiz: Can you tell which line or lines in this Java program will cause a compiler error:

  File: /home/cs255001/demo/java/JavaExprEval.java public class JavaExprEval { public static void main(String[] arg) { byte b1 = 44, b2 = 22; short s; s = b1; // Will this statement cause an error ? s = b1+b2; // Will this statement cause an error ? } }

  The answer is below...

   

   

   

   

   

   

   

   

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  • When you use different data types in an operation, the computer must perform conversion to make the types equal

    In other words: one code (= representation) must be converted into another code (= representation) before the operation can take place.

  • In CS170/CS171, you may have remember (I'm sure the professor mentioned it) the following (partial) safe conversion:

    Java's safe conversions: byte ---> short ---> int

    You may also remember that:

    In Java, all (integer) operations performed on integer values are done using the int data type

    That means:

    If you use a byte typed (8 bits 2s complement code) of short typed (16 bits 2s complement code) value in some expression, the Java compiler will first convert it (= the code used) into the corresponding int typed

    See if you can apply this Java rule and figure out what's going on in this program.

    File: /home/cs255001/demo/java/JavaExprEval.java public class JavaExprEval { public static void main(String[] arg) { byte b1 = 44, b2 = 22; short s; s = b1; // Will this statement cause an error ? s = b1+b2; // Will this statement cause an error ? } }

     

     

     

    Answer:

    cheung@aruba> javac JavaExprEval.java JavaExprEval.java:12: error: incompatible types: possible lossy conversion from int to short s = b1+b2; // Error, because Java converts byte to int before adding ^ Explanation: s = b1; // Is OK. Because: there is no operation performed. // The byte b1 can be converted safely to a short and assigned to s s = b1+b2 // Error. Because: there is a + operation ! // So the byte b1 is converted to int representation, and // the byte b2 is converted to int representation, then // the int values (representations) are added // The final result is int (32 bits) // But an int cannot be safely converted to a short (s) !!!

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• How to convert (cast) a byte representation to an int representation
  • It is very easy to convert a byte (8 bit 2s complement code) to an int (32 bits 2s complement code(:

    To convert a byte (8 bit 2s complement code) to an int (32 bits 2s complement code(, you extend the sign bit of the byte The sign bit is the left-most bit in the byte representation We call this operation: sign extension

    Examples:

    Value byte (8 bits 2s compl code) int (32 bits 2s compl code) ------- ---------------------------- ---------------------------------- 127 01111111 00000000000000000000000001111111 ... 3 00000011 00000000000000000000000000000011 2 00000010 00000000000000000000000000000010 1 00000001 00000000000000000000000000000001 0 00000000 00000000000000000000000000000000 -1 11111111 11111111111111111111111111111111 -2 11111110 11111111111111111111111111111110 -3 11111101 11111111111111111111111111111101 ... -128 10000000 11111111111111111111111110000000

    Notice that:

    The lower 8 bits in the int representation is equal to the original byte representation !!! That means: We can obtain the byte representation from an int representation by: Discarding the left-most 24 bits in the int representation In fact, this is how int --> byte casting works !!! How to convert (cast) int --> byte: Discard the left-most 24 bits in the int representation

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    Quiz on int --> byte casting:

    Given that: 4100 (decimal) is represented by the 2s complement code 00000000000000000001000000000100. What is the value of the byte variable b in this statement: int i = 4100; byte b; b = (byte) i;

    Answer:

    b = (byte) i will assign 00000100 to b 00000100 represents the value 4

    To show you that this is the correct answer, I have written this Java program:

    /home/cs255001/demo/java/JavaByteIntCast.java

    I will compile and run it in class. You can try it out yourself if you did not attend class....

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• How to convert (cast) a byte representation to an int representation
  • It is also very easy to convert a short (16 bit 2s complement code) to an int (32 bits 2s complement code(:

    To convert a short (16 bit 2s complement code) to an int (32 bits 2s complement code(, you extend the sign bit of the byte

    Examples:

    Value short (16 bits 2s compl code) int (32 bits 2s compl code) ------- ---------------------------- ---------------------------------- 32767 0111111111111111 00000000000000000111111111111111 ... 3 0000000000000011 00000000000000000000000000000011 2 0000000000000010 00000000000000000000000000000010 1 0000000000000001 00000000000000000000000000000001 0 0000000000000000 00000000000000000000000000000000 -1 1111111111111111 11111111111111111111111111111111 -2 1111111111111110 11111111111111111111111111111110 -3 1111111111111101 11111111111111111111111111111101 ... -32768 1000000000000000 11111111111111111000000000000000

    Notice that:

    The lower 16 bits in the int representation is equal to the original short representation !!! That means: We can obtain the short representation from an int representation by: Discarding the left-most 16 bits in the int representation In fact, this is how int --> short casting works !!! How to convert (cast) int --> short: Discard the left-most 16 bits in the int representation

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    Quiz on int --> short casting:

    Given that: 262150 (decimal) is represented by the 2s complement code 00000000000001000000000000000110. What is the value of the short variable b in this statement: int i = 262150; short s; s = (short) i;

    Answer:

    s = (byte) i will assign 0000000000000110 to s 0000000000000110 represents the value 6

    To show you that this is the correct answer, I have written this Java program:

    /home/cs255001/demo/java/JavaShortIntCast.java

    I will compile and run it in class. You can try it out yourself if you did not attend class....