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Boolean Algebra

Discussion in 'Electronic Basics' started by Beanq, Oct 19, 2003.

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  1. Beanq

    Beanq Guest

    How can I simplify this? I need to implement it using NAND gates only. I
    thought maybe Demorgan, but I don't see how.
    F=AB+AC+AD+BC+BD+CD
     
  2. CFoley1064

    CFoley1064 Guest

    How can I simplify this? I need to implement it using NAND gates only. I
    Hi, Bean. Straight homework help here. Cool.

    Beginning digital logic classes are given three tools -- truth table, Karnaugh
    mapping, and Demorgan, right? First thing I did was just draw a truth table.
    Inspection shows there are only five cases where F is not true, so I decided to
    do this inverted -- that is, solve for what's not true, rather than what's
    true.

    Let Q = (A! AND B! AND C!)
    Let R = (A! AND B! AND D!)
    Let S = (A! AND C! AND D!)
    Let T = (B! AND C! AND D!)

    It should be obvious looking at the table that F! = Q + R + S + T (with A! AND
    B! AND C! AND D! being the redundant case which is true for all). Now, you can
    Demorganize that, and come up with what you have below, with the last NAND
    being used to invert again from F! to F. View in fixed font (like M$
    Notepad)...

    .---.
    A!----| |
    B!----| |o----------
    C!----|& | |
    | | |
    '---' |
    .---. |
    A!----| | | .-----.
    B!----| |o------- | | |
    D!----|& | | '-- | | __
    | | | | | |-----| |
    '---' '----- | |o------| |& |o-
    .---. | & | ------|__|
    A!----| | .------| |
    C!----| |o------- | |
    D!----|& | .---| |
    | | | '-----'
    '---' |
    .---. |
    B!----| | |
    C!----| |o----------
    D!----|& |
    | |
    '---'

    created by Andy´s ASCII-Circuit v1.22.310103 Beta www.tech-chat.de

    This is pretty similar to factoring quadratics back in high school -- your
    ability improves with practice. Try solving problems in different ways, and
    just do what works.

    Good luck.
    Chris
     
  3. Looks like schoolwork. But nevertheless:

    It's (almost) written in NANDS and there is nothing to simplify. (Just draw
    a Karnaugh map to see it.) Just use De Morgan:

    f=ab+ac+ad+bc+bd+cd
    =//(ab+ac+ad+bc+bd+cd)
    = /(/(a*b) * /(a*c) * /(a*d) * /(b*c) * /(b*d) * /(c*d))

    So you need six two inputs NAND and one six inputs NAND.

    (N)AND that's it.

    pieter
     
  4. SHAUN

    SHAUN Guest

    chris wrote:

    Shaun writes: great answer!, even though I don't understand one word you
    wrote, but it did sound great
     
  5. Baphomet

    Baphomet Guest

    It must be those cheesy ASCII representations Shaun ;-) I don't think
    anybody understands them with the possible exception of the poster!
     
  6. You are using Outlook Express and it is not easy to see the ASCII
    schematics in it.

    You need to right-click the message in the message list, choose
    "properties", details, source code, maximize window. then you will see
    the message in notepad, with a fixed font, and these ASCII schematics
    will make sense to you.
     
  7. Baphomet

    Baphomet Guest

    Thanks for the tip Roger -

    I guess I'm just old fashioned. I still prefer a good schematic but I'll try
    your advice ;-)
     
  8. It works, if you only try to do it step by step.
    First rightclick the message, and choose properties at the bottom of
    the menu which appears, then choose the "details tab" at the top of
    that window, then use the button named source (there is only one
    button there so it doesn't matter what it says really), and maximize
    that new popup window. There is the raw message and it starts with a
    lot of headers, scroll down to see the real message.
     
  9. Baphomet

    Baphomet Guest

    I'm still too stupid to figure out how to do this in O.E., but I did look at
    the post in Google and it made perfect sense, even to a dolt like me...DUH
     
  10. Lord Garth

    Lord Garth Guest

    In OE, one clicks 'view' then 'text size' then 'fixed'.
    One can also set the default font to couier ....
     
  11.  
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