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Math Help - Boolean eqn from table ques.

  1. #1
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    Boolean eqn from table ques.

    Hi everyone,

    Can someone help me with this..I dont know where to start.


    Write the Boolean Equation that corresponds to the Truth Table as below:
    A B C Z
    0 0 0 1
    0 0 1 0
    0 1 0 1
    0 1 1 0
    1 0 0 1
    1 0 1 0
    1 1 0 1
    1 1 1 0

    Pls help guide and advise...tq so much,really appreciate it.

    Tq & rgds.
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  2. #2
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    Hello anderson!

    Quote Originally Posted by anderson View Post
    Hi everyone,

    Can someone help me with this..I dont know where to start.


    Write the Boolean Equation that corresponds to the Truth Table as below:
    A B C Z
    0 0 0 1
    0 0 1 0
    0 1 0 1
    0 1 1 0
    1 0 0 1
    1 0 1 0
    1 1 0 1
    1 1 1 0

    Pls help guide and advise...tq so much,really appreciate it.

    Tq & rgds.
    I assume Z represents the result?

    First of all i considered

    0 0 0 => 1
    and
    1 1 1 => 0

    So I thought at neq(A and B and C) = neq (0) = 1
    and neq(A and B and C) = neq(1) = 0

    The second line says

    0 0 1 => 0.

    neq(A and B and C ) = neq(0 and 0 and 1) = neq(0) = 1

    That is wrong already. So i modified the guess to neq((A and B) or C)
    In this case it is neq((0 and 0) or1) = neq(1) = 0

    neq((A and B) or C) solves the tableau, iff Z is the result.

    In this case it is much easier, because neq(C) would solve the table as well. But that seems too easy. What does Z mean?

    Yours
    Rapha
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  3. #3
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    Hi Rapha/everyone

    Sorry, Z is the output/result.


    Thank you for all your help & support...pls help me im stuck.

    Tq & rgds
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  4. #4
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    Hey!

    Quote Originally Posted by anderson View Post
    Hi Rapha/everyone

    Sorry, Z is the output/result.
    Okay


    Quote Originally Posted by anderson View Post
    Thank you for all your help & support...pls help me im stuck.

    Tq & rgds
    What exactly is the question?
    Furthermore are you sure there is no typo in your table?

    You wrote

    A B C Z
    0 0 0 1
    0 0 1 0
    0 1 0 1
    0 1 1 0
    1 0 0 1
    1 0 1 0
    1 1 0 1
    1 1 1 0


    Lets consider the C-column and the Z-column:

    C Z
    0 1
    1 0
    0 1
    1 0
    0 1
    1 0
    0 1
    1 0

    Thus the boolean equation for Z is C (it is the negation of C.)
    Negation of 1 is 0
    Negation of 0 is 1

    You don't even need the A-terms or the B-terms in your bool equation.

    kind regards
    Rapha

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  5. #5
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    Hi everyone
    Here is the question:

    Write the Boolean Equation that corresponds to the Truth Table as below:

    A B C Z
    0 0 0 1
    0 0 1 0
    0 1 0 1
    0 1 1 0
    1 0 0 1
    1 0 1 0
    1 1 0 1
    1 1 1 0

    pls help me...tq so much for all your comments & guidance,really appreciate it.
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  6. #6
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    Hello anderson!

    Quote Originally Posted by anderson View Post
    Hi everyone
    Here is the question:

    Write the Boolean Equation that corresponds to the Truth Table as below:

    A B C Z
    0 0 0 1
    0 0 1 0
    0 1 0 1
    0 1 1 0
    1 0 0 1
    1 0 1 0
    1 1 0 1
    1 1 1 0

    pls help me...tq so much for all your comments & guidance,really appreciate it.
    What is wrong with C ? It is possible that you prefer C' or C^c instead of C.
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  7. #7
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    Hi Rapha

    i wanted the answer using K-mapping technique....ur answer is also correct.tq..

    Tq & rgds
    Last edited by anderson; August 7th 2009 at 12:37 PM.
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  8. #8
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    Hey!

    Quote Originally Posted by anderson View Post
    Hi Rapha

    i wanted the answer using K-mapping technique
    I'm sorry, because I didn't know that.
    If you still want to find the solution by using K-mapping technique click this
    Karnaugh Maps

    I think Table 1-17 and Table 1-18 are very helpful.And it is very similar to your problem.

    Kind regards
    Rapha
    Last edited by Rapha; August 7th 2009 at 10:30 PM.
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  9. #9
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    Eqn from table answer....

    Hi Rapha/everyone,

    This is the full answer:

    By summing the minterms of output which is high
    Z = m₀ + m₂ + m₄ + m₆
    Z=ABC + ABC+ABC+ABC

    Simplifying the equation:
    Z=AC(B+B)+AC(B+B)
    =AC+AC
    =C(A+A)
    =C
    [
    thank everyone for your help & advise...
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  10. #10
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    Hello, anderson!

    Is it as simple as I think it is?


    Write the Boolean Equation that corresponds to the Truth Table below:

    . . \begin{array}{|c|c|c|| c|}<br />
A & B & C &Z \\ \hline <br />
0 &0& 0 &1 \\<br />
0& 0& 1 &0 \\<br />
0& 1& 0& 1 \\<br />
0 &1 &1 &0 \\<br />
1 &0 &0 &1 \\<br />
1 &0 &1 &0 \\<br />
1 &1 &0 &1 \\<br />
1 &1 &1 & 0<br />
\end{array}

    The Z-values are the opposite of the C-values.
    . . (The A- and B-values are irrelevant.)

    The equation would be: . Z \:=\:\overline{C}

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  11. #11
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    Hi everyone

    The question wanted the root equation before it is simplified as well.The root equation can be derived from the table using minterms.

    thank you to everyone for responding,really appreciate all your help & support.

    Tq & rgds
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