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Representing boolean values inside the computer

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• The (all possible) Boolean values
  • I start with representing the Boolean values because it is easy and intuitive

  • There are only 2 Boolean values:

    true false

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• Representing the Boolean values
  • A representation is a encoding system that allow you to associate a set of values uniquely using the encoding system

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  • When we need to represent the Boolean values inside a computer, we must make a association between these 2 sets of values:

    Boolean values Values stored by the computer -------------------- --------------------------------- false 00000000 true 00000001 00000010 00000011 ...

    The association that many (if not all) computer programming languages use is the following:

    Boolean values Values stored by the computer -------------------- --------------------------------- false <--------> 00000000 true <--------> 00000001 true <--------> 00000010 true <--------> 00000011 ... ...

    I.e.: the Boolean value false is represented by the binary number 00000000.

    The Boolean value true is associated with all non-zero binary numbers

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• Example of Boolean representation in the Python programming language
  • I can illustrate the above Boolean representation method using the Python programming language (because Python uses the above method to represent Boolean values).

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  • To run this experiment, you need Python installed on your laptop or login to a lab machine

    The following Python program:

    /home/cs255001/demo/Python/Boolean/boolean.py if 0: print("0: true") else: print("0: false") if 1: print("1: true") else: print("1: false") if 4: print("4: true") else: print("4: false")

    will output:

    cheung@lab1a> python boolean.py 0: false 1: true 4: true

    which shows you that Python uses the following Boolean to integer encoding:

    Boolean values Values in Python -------------------- --------------------------------- false <--------> 00000000 (= 0) true <--------> 00000001 (= 1) true <--------> 00000010 (= 2) true <--------> 00000011 (= 3) true <--------> 00000100 (= 4) ... ...

    I highlighted the partial association printed by the Python program in red