Help with Boolean Algebra Simplification

Discussion in 'Homework Help' started by Emile_Uk, Nov 17, 2003.

  1. Emile_Uk

    Thread Starter New Member

    Nov 17, 2003

    If anyone can help me simplify the following two boolean expressions whilst listing the laws used at each stage then that would be hugely appreciated!

    The two expressions are:




    Where * is AND and [] is an inverted input.

    Any help would be greatly appreciated!


  2. Dave

    Retired Moderator

    Nov 17, 2003
    Firstly the second one (because its easier):


    Deal with the first two brackets and take out P*[X]*Y as common factors

    Therefore: P*[X]*Y([Q]+Q) where [Q]+Q = 1 (Complementary Law)

    So that gives (P*[X]*Y) + (P*Q*X*[Y]) (with the third bracket reintroduced)

    Now take out P as a common factor:

    So you get P*{([X]*Y) + (Q*X*[Y])}

    Thats it in its simplest form.

    The first one is considerably more difficult:


    Look at brackets 3 and 4 and take out P*[Q]*X as common factors

    So P*[Q]*X([Y]+Y) where [Y]+Y = 1

    Do the same with brackets 5 and 6 taking P*Q*Y out as common factors

    So P*Q*Y([X]+X] where [X]+X = 1

    Brackets 1 and 2 are just take out [P]*Q as common factors and get:


    So your answer should now look something like:

    [P]*Q*{([X]*Y) + (X.[Y])} + (P*[Q]*X) + (P*Q*X)

    Take out common factors of P*X in the last two expresions to get P*X([Q]+Q) where [Q] + Q = 1 and just gives P*X

    Your final answer should look like:

    [P]*Q*{([X]*Y) + (X.[Y])} + P*X

    I haven't had chance to look at this with another method but will post back if the answer comes out any different. I'd also appreciate comments on any errors I have made or if you'd like any further help :)