‘Binary 1+1 and Boolean 1+1 are not same’ –Explain.ī. In which argument 1+1=1 and 1+1=10 can be written? –Explain.ī. আরো পড়ুন :: Sixth Chapter: Comprehension Based Questions & Answers.ī. Lesson Evaluation- Knowledge Based Questions: Proof of Some Basic Boolean Theorems: In case of Boolean Addition: Idempotent law – a variable remain unchanged when it is ORed or ANDed with itself, i.e.,Ĭomplement law – in this Law if a complement is added to a variable it gives one, if a variable is multiplied with its complement it results in ‘0’, i.e.,ĭouble negation law – a variable with two negation its symbol gets cancelled out and original variable is obtained, i.e.,Ĭommutative law – a variable order does not matter in this law, i.e.,Īssociative law – the order of operation does not matter if the priority of variables are same like ‘*’ and ‘/’, i.e.,ĭistributive law – this law governs opening up of brackets, i.e.,Ībsorption or Secondary law –:-This law involved absorbing the similar variables, i.e.,Ī+A’B = A+B Switching Circuits for Boolean Theorems: Boolean Identity law – in this law variable remain unchanged it is ORed with ‘0’ or ANDed with ‘1’, i.e., We can verify all these Boolean equations of Group1 and Group2 by using duality theorem.Īnnulment law – a variable ANDed with 0 gives 0, while a variable ORed with 1 gives 1, i.e., In each row, there are two Boolean equations and they are dual to each other. The following table shows these two groups. Let us make the Boolean equations r e l a t i o n s that we discussed in the section of Boolean postulates and basic laws into two groups. আরো পড়ুন :: What is Biometric? Types of Biometric | Uses of Biometric ![]() For every Boolean function, there will be a corresponding Dual function. This theorem states that the dual of the Boolean function is obtained by interchanging the logical AND operator with logical OR operator and zeros with ones. Note− The complement of complement of any Boolean variable is equal to the variable itself. Complement of 1 is 0 and Complement of 0 is 1. The rules followed by NOT Operation ( Logical Inversion) in Boolean Algebra is called Boolean Postulates of NOT. The rules followed by AND Operation (Logical Multiplication) in Boolean Algebra is called Boolean Postulates of AND. The rule is – If any value among values is 0, result will be 0, Otherwise result will be 1. ![]() The rule is – If any value among values is 1, result will be 1, Otherwise result will be 0. The rules followed by OR Operation ( Logical addition) in Boolean Algebra is called Boolean Postulates of OR. The rules followed by OR Operation ( Logical addition), AND Operation (Logical Multiplication) and NOT Operation ( Logical Inversion) in Boolean Algebra is called Boolean Postulates. Boolean Postulates are three types. It is possible to solve all the mathematical and logical problems in digital devices by converting logic TRUE and logic FALSE of Boolean algebra into 1 and 0 respectively. This Boolean algebra is used in these digital devices to solve mathematical and logical problem. On the other hand all kind of digital devices work in binary method. ![]() ![]() It is also called as Binary Algebra or logical Algebra or Switching algebra. A mathematician, named George Boole discovered a relation between mathematics and logic, based on this relation he developed a kind of algebra in 1854 called Boolean algebra.īoolean algebra basically developed based on logic TRUE and logic FALSE. Boolean Algebra is used to analyze and simplify the digital (logic) circuits. You will be able to explain different Boolean Theorems.īoolean Algebra is an algebra, which deals with binary numbers & binary variables.You will be able to explain Boolean postulate and Duality Principle.You will be able to explain Boolean variable, constant and complement.You will be able to explain the characteristics of Boolean Algebra.
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |