E.SURIYA

  CONONICAL FORMS The use of switching devices like transistors give rise to a special case of the Boolean algebra called as switching algebra. In switching algebra, all the variables assume one of the two values which are 0 and 1. In Boolean algebra, 0 is used to represent the ‘open’ state or ‘false’ state of logic gate. Similarly, 1 is used to represent the ‘closed’ state or ‘true’ state of logic gate. A Boolean expression is an expression which consists of variables, constants (0-false and 1-true) and logical operators which results in true or false. TWO TYPE OF CONONICAL FORMS; A Boolean function is an algebraic form of Boolean expression. A Boolean function of n-variables is represented by f(x1, x2, x3….xn). By using Boolean laws and theorems, we can simplify the Boolean functions of digital circuits. A brief note of different ways of representing a Boolean function is shown below. Sum-of-Products (SOP) Form Product-of-sums (POS) form Canonical forms There are two types of can...

 BOOLEN ALGEBRA                      George Boole , (born November 2, 1815, Lincoln,  Lincolnshire , England—died December 8, 1864, Ballintemple, County  Cork , Ireland), English mathematician who helped establish modern symbolic  logic  and whose algebra of logic, now called  Boolean algebra , is basic to the design of  digital computer  circuits.                        INTRODUTION; The most obvious way to simplify Boolean expressions is to manipulate them in the same way as normal algebraic expressions are manipulated. With regards to logic relations in digital forms, a set of rules for symbolic manipulation is needed in order to solve for the unknowns. A set of rules formulated by the English mathematician  George Boole  describe certain propositions whose outcome would be either  true  or  false . With re...