Digital electronics problem

Discussion in 'General Electronics Chat' started by zachary, Jan 8, 2013.

  1. zachary

    Thread Starter New Member

    Jan 8, 2013
    6
    0
    I have this problem and i'm looking for someone to please tell me how to write the truth table because i'm confused by the word adjacent.
    Four chairs A,B,C and D are placed in a row . Each chair may be occupied ('' 1'') or empty ("0 ") . A Boolean function F is "1" if and only if there are two or more adjacent chairs that are empty .Give the truth table.
     
  2. tshuck

    Well-Known Member

    Oct 18, 2012
    3,531
    675
    Adjacent means the chairs are next to each other. A is adjacent to B, B is adjacent to both A and C, C is adjacent to both B and D, D is adjacent to C...

    This is a bit of an odd question, but the point is valid:

    Write a set of states that represent all possible states of the chairs and what the truth value is on the other side:

    States
    A B C D Output
    0 0 0 0 1 (adjacent chairs are empty)
    0 0 0 1 1 (adjacent chairs are empty)EDIT:eek:riginally said "no adjacent chairs are empty", which is just silly:p
    ... ...
    1 0 1 0 0 (no adjacent chairs are empty)
    ... ...
    1 1 1 1 0 (no adjacent chairs are empty)
     
    Last edited: Jan 8, 2013
    zachary likes this.
  3. WBahn

    Moderator

    Mar 31, 2012
    17,757
    4,800
    You've got a typo in the second line of the partial truth table for the case of 0001. You state that the output is 1 (which is correct) but say that no adjacent chairs are empty when there are two pairs of adjacent chairs that are empty. I'm sure it's just a slip of the fingers.

    If I am counting correctly, there should be 8 rows in the table that have a True output.

    Another way to approach the problem is to solve it directly. How many pairs of adjacent chairs are there? What is the logic function that will tell if a given pair of adjacent chairs are both empty? How can this be combined to detect if at least one pair of adjacent chairs are empty? From this you can draw the circuit and, from that, fill in the truth table and compare it to the brute force solution.
     
    zachary likes this.
  4. tshuck

    Well-Known Member

    Oct 18, 2012
    3,531
    675
    Whoops! I got carried away with the ctrl+c/v:p Fixing it now...
     
    zachary likes this.
  5. ErnieM

    AAC Fanatic!

    Apr 24, 2011
    7,392
    1,606
    As much as I prefer truth tables this problem seems to better lend itself to a Boolean function.

    Consider chairs A and B: These are adjacent and only unoccupied when both A and B are 0:

    A' * B' (using ' to denote inversion)

    A similar argument may be made for B and C, and C and D:
    B' * C'
    C' * D'

    The output is true is any of these sub terms is true, so they or:

    OUT = (A' * B') + (B' * C') + (C' * D' )

    This function can be realized with a handful of gates (3 2-in NOR and 1 3-in OR)
     
    zachary likes this.
  6. WBahn

    Moderator

    Mar 31, 2012
    17,757
    4,800
    Guys! Come on. This is clearly some kind of homework problem. Should we really just be giving out solutions all wrapped up with a bow? Shouldn't the OP be asked to do some thinking about it?
     
    zachary likes this.
  7. tshuck

    Well-Known Member

    Oct 18, 2012
    3,531
    675
    The question does not relate directly to electronics, and, as such, it must be a learning exercise as to how to think and make a truth table.

    I didn't fill the whole thing in because I wanted the OP to take the time to fill it in while examining the reasoning for the answers given. I think that at this stage of understanding the truth table, the only thing to do is look at how it's done and why...
     
    zachary likes this.
  8. zachary

    Thread Starter New Member

    Jan 8, 2013
    6
    0
    Thanks to all those who contributed to my problem and I really appreciate your contributions. My problem is now solved.
     
Loading...