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The compiler translates every number in your program into a 2s complement binary representation

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• A very important programming pre-requisite before we start discussing the conversion algorithm
  • Very important that you understand this:

    When you write a Java statement that uses an integer value v: The Java compiler will translate the integer value v to its corresponding 2's complement code

    In other words:

    When you write this Java statement: short x; x = 3; Java compiler will generate machine instruction to: Store the 2's complement number 0000000000000011 in variable x

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  • Furthermore, the Java statements/expressions that you write in human-readable (decimal) form, the computations are performed in binary (courtesy from your Java compiler !)

    In other words:

    When you write this Java statement: x = x + 2; The variable x contains a binary number and the number 2 is translated into the binary number 0000000000000010. And the Java compiler will generate machine instruction to: Add 0000000000000010 to the binary number in x // using binary addition !! (And store the resulting binary number back in the variable x)