Need a little help

Discussion in 'Homework Help' started by carnage123, Feb 18, 2006.

  1. carnage123

    Thread Starter New Member

    Feb 18, 2006
    7
    0
    Hi everyone, I'm new to this forum. I've been learning from the online texts but never noticed this forum.

    Anyways, I'm learning Digital right now and have a few questions.

    So far, I know about the logic gates, the SL chips, boolean algebra, converting to hexadecimal, decimal, octal to binary (and reverse) and truth tables. The only thing I'm confused about is using combinations of logic gates. When I'm using a logic trainer and IC's I'm able to understand it through application. But I have no clue as to how to draw this stuff on paper. What steps do you take to build something using a combination of gates.

    Lets take this for example; if ALL "gear" "flaps" and "speed" are "1" or hi the green light goes on, if any of these are lo or "0" then the buzzer goes off and a red light goes on. What steps should I take to build this kind of scenario. Do I first look at the truth tables, logic gates and then connect them. Whats a good way to combine logic gates together?

    Secondly, I'm learned about HD and Octal conversions, how does this stuff apply to digital electronics. Can you give me a few examples of how this would apply?

    Thanks alot for any responses!
     
  2. carnage123

    Thread Starter New Member

    Feb 18, 2006
    7
    0
    wow, that was extremely helpful, thanks for notin everyone.
     
  3. Gadget

    Distinguished Member

    Jan 10, 2006
    613
    0
    just a 3 input AND gate and some buffers to drive the LED's and Buzzer would do it.
    i.e ALL inputs must be high before the output will go high.
    if any input goes low, then so will the output.
    One buffer could then drive a buzzer, and another could drive both LED's by "sourcing" the green LED and "sinking" the red.
     
  4. n9352527

    AAC Fanatic!

    Oct 14, 2005
    1,198
    3
    There are many ways to get the circuit from specifications. You could always do it from a truth table and work on all the terms that have '1' as outputs. These would result in sum of products equations.

    You could also obtain the equations from karnaugh maps which makes it easier to simplify the equation and eliminate glitches. Search on this allaboutcircuits.com site for karnaugh map.

    From your example above, the output would only be one when gear, flaps and speed are one. Ignoring all the output that are 0, then: Output = Gear AND Flaps AND Speed. So you need one three-input AND gate, or cascade of three 2-input AND gate.
     
  5. carnage123

    Thread Starter New Member

    Feb 18, 2006
    7
    0
    Sorry bout my second post, I was completely lost about the answer so I was pritty anxious to find out. Anyways, thanks for the replies, those really did help!
     
  6. Papabravo

    Expert

    Feb 24, 2006
    9,898
    1,722
    The key insight about combinatorial logic functions (those with no memory) made from AND and OR and NOT gates is that ALL logic functions can be realized with only two levels of gates. From a truth table, each input which is a zero corresponds to taking the complemnt(NOT) of the input to an AND gate, and each input which is a one corresponds to taking the input itself to the AND gate. Use a separate AND gate for each row in the truth table which produces an ontput of one. Forget about the rows for which the output is zero.

    The set of AND gates is level one. Now take the output of each AND gate and run it to one of the inputs of a single multple input OR gate. The single multiple input OR gate is level 2. This is called a "sum-of-products" form.

    If you can wrap your arms around this explanation, then you should be able to convince yourself that there must also be a "product-of-sums" form and you would be correct!

    On your question about alternate number bases such as hexidecimal and octal; they are convenient ways of talking about groups of bits in which the conversion between binary and octal or hexidecimal can be done in your head without thinking about it. This is because there is a rote pattern substitution that, once learned, is foolproof. I don't know anybody who can write down the binary equivalent of 7,233 decimal without using a calculator or pencil and paper. I know lots of people who can write the binary equivalent of 0xBAAD. Octal is a holdover from computers with a data word length or address bus length divisible by three like the DEC PDP-10, PDP-11, and the IBM 7094. Hexidecimal is used where the data word length or the address bus length is a multiple of 4 bits.
     
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