Hi Guys, I have some boolean problems, and if you can solve it ... just do it 1)Write the dual of each Boolean expression. (Insert parentheses so that the result is properly interpreted.) a) A + B . C b) A . (B + C) + (A(B . C) c) A + B + (A + B) .C + (A + B + C) . D _______________________________________________ 2) Use the axioms and theorems of Boolean algebra to prove the following theorems. a) (A . B) + (A . B) = A b) (A . B) + (A . C) + (B . C) = A . C c) AB + AB = (A + B) . (A + B) = (A + B) . (AB) d) A + A . B . C = A + B . C _______________________________________________ 3) The following expressions are difficult to read as written. Insert Parentheses to clarify them by identifying the operator hierarchy in each function. a) A + B. C + D . E b) A . B + C . D + E + F c) A . B + C . (D + E . F) ________________________ Let us share the solution
The dual equation can be obtained by replacing the following: + with . . with + 0 with 1 1 with 0 The principle of duality does not mean that the dual equation must equal the original equation. However, the dual equation must be valid for all values of it's variables. Example: The dual of: A + A' = 1 is A . A' = 0 However the dual of A + B = 1 is not A . B = 0 because if A = 1 and B = 1, then A . B is not equal to 0. Therefore A . B = 0 is not a valid equation. If you need a clear explanation of any other concept, ask. If you accept a job in engineering, then understanding these concepts may be important. Boolean algebra can be used to design some digital circuits. Sometimes a circuit designed with boolean algebra yields less components than the same circuit designed without boolean algebra. You are making a mistake trying to have someone else do your homework for you.
Thank you for your support. The problem is that I didnt understand the boolean algebra as I think I should do,, what I mean is I need to know how I can deal with boolean problems, knowing the solution key is the most important thing that I need. However, I did solve these problems but I need to double check the answer. So, can I show you my answers to correct them or maybe you can tell me how I can do them well. Thank you again, and really in these days I need some one who can leed me to the correct direction in boolean algebra.
Can I suggest you have a look at our chapter on Boolean Algebra: http://www.allaboutcircuits.com/vol_4/chpt_7/index.html It has all of the underlying theory of Boolean Algebra and all identities you will need for every equation you will do. Furthermore, can I suggest you download m4yh3m's superb cheat sheets. Dave