Can someone please help me with this logic circuit problem?

I need step by step explanation and solution to this question please, so I can answer others.


In the set of inputs a,b,c,
in the case there are 2 or more numbers of '1' in the set, it is designated 1, or else, it is designated 0.
Consider that logical function f above.

1. Draw the truth table for f.
2. Find the simplest product-of-sum expression for f.

Replies

  • Jeffrey Arulraj
    Jeffrey Arulraj
    Here this should help
    A B C F max terms
    0 0 0 0 A+B+C
    0 0 1 0 A+B+C'
    0 1 0 0 A+B'+C
    0 1 1 1
    1 0 0 0 A'+B+C
    1 0 1 1
    1 1 0 1
    1 1 1 1

    So the final expression for f is

    f=(A+B+C).(A+B+C').(A+B'+C).(A'+B+C)

    Do simplify it further if you want to friend
  • Aruwin
    Aruwin
    jeffrey samuel
    Here this should help
    A B C F max terms
    0 0 0 0 A+B+C
    0 0 1 0 A+B+C'
    0 1 0 0 A+B'+C
    0 1 1 1
    1 0 0 0 A'+B+C
    1 0 1 1
    1 1 0 1
    1 1 1 1

    So the final expression for f is

    f=(A+B+C).(A+B+C').(A+B'+C).(A'+B+C)

    Do simplify it further if you want to friend
    How to further simplify this function?
    f= a'bc+ab'c+abc'+abc
    = c(a'b + ab') + ab (c' + c)
    =c(a'b + ab') + ab
    I only got it up to here. How to simplify it into the most simple expression?
  • Vishal Sharma
    Vishal Sharma
    Aruwin
    How to further simplify this function?
    f= a'bc+ab'c+abc'+abc
    = c(a'b + ab') + ab (c' + c)
    =c(a'b + ab') + ab
    I only got it up to here. How to simplify it into the most simple expression?

    I don't think you can simplify it further..
    the next step will be writing XOR expression instead of a'b+ab'
    i.e. c (a XOR b) + ab

    (You can replace the XOR by this sign too)

    xor-symbol.thumbnail
  • Jeffrey Arulraj
    Jeffrey Arulraj
    I think this is the most simplified form the Answer can ever get

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