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How does one form an equation for adder/subtractor?

  1. Jan 19, 2017 #1
    I understand the concept of Kmaps, Quine method and forming a logic diagram but I'm lost at forming an equation from an addition and subtraction equation

    For example: a 2 bit plus a 3 bit binary integer. I would have a 4 bit sum and 3 carries. However, how does one form the appropriate equation in order to convert it to a proper logic circuit?
  2. jcsd
  3. Jan 19, 2017 #2


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    Staff: Mentor

    Write a truth table for each output based on the inputs. Then do a K-map for each of the outputs and design the logic from the minterms... Can you show us what you have been reading about how to do this? :smile:
  4. Jan 19, 2017 #3


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    Science Advisor

  5. Jan 20, 2017 #4
  6. Jan 21, 2017 #5
    So these sites currently


    Nobody explains how the truth table for multiple bits work. I assume they're half adders and full adders clumped together but how to form an equation from it? Like where did the AND gate come from? And why put the AND gate for the carries separately instead of putting it in one 3 input AND gate for the 3 bit addition?
    Last edited: Jan 21, 2017
  7. Jan 22, 2017 #6


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    The answer to both questions: Write up the addition and subtraction tables completely with carry and borrow. Then deduce the logical gate combination.
    Oh, yes they do. Start with https://en.wikipedia.org/wiki/Truth_table
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