![]() Here the truth values represent the relation of a proposition to truth, that is, whether the proposition is true or false.Ī proposition is just a statement like "All cats are cute." The underlying meaning behind truth values comes from field of Logic where truth values are used to tell if a proposition is "True" or "False". Now the question is that if (True and False), (0 and 1) are just the representations, then what is it that they are trying to represent? But make sure that you don't change the symbols while performing the operations. The point here is that the internal meaning of these symbols will remain the same irrespective of the symbol you use. You can also do it in more fancy ways by representing truth values with some other symbols such as Cats and Dogs or Bananas and Oranges. Here, I would like to point out the fact that we can use any other symbol to represent these values.įor example in Computer Science we mostly represent these values using 0 and 1. The Truth values, in comparison, consist of a set of only two values: False and True. Ordinary Algebra deals with this entire set of numbers. The set of Real numbers includes Natural numbers(1, 2, 3, 4.), Whole numbers (all the Natural numbers and 0), Integers (.-2, -1, 0, 1, 2, 3. The image below shows the entire set of Real numbers. In case of ordinary Algebra, the symbols represent the Real numbers whereas in Boolean Algebra they represent the Truth values. It is this quantity that gives some value to these symbols and it is this quantity on which the operations are actually being performed.īoolean Algebra also deals with symbols and the rules that govern the operations on these symbols but the difference lies in what these symbols represent. These symbols do not have a meaning of their own. ![]() To best understand Boolean Algebra, we first have to understand the similarities and differences between Boolean Algebra and other forms of Algebra.Īlgebra, in general, deals with the study of mathematical symbols and the operations that can be performed on these symbols. These sets of foundations led to the development of Boolean Algebra. These rules gave a mathematical foundation for dealing with logical propositions. In his 1854 book, British Mathematician George Boole proposed a systematic set of rules for manipulation of Truth Values. The rules I mentioned above are described by a field of Mathematics called Boolean Algebra. In this article we will discuss those rules and we will see how they govern the way computers "think". There are rules that govern the way this should be done. There is indeed some reasoning behind it. ![]() It is remarkable to see how such a simple action can lead to so much complexity.īut I'm sure you all know that such complexity cannot be achieved (practically) by just randomly flipping the numbers. They can do tasks of varying degrees of sophistication, all by just flipping zeros and ones. Within a couple of decades computers have completely revolutionized almost all the aspects of human life.
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