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Combinational circuit that multiplies two numbers together

  1. Sep 21, 2015 #1
    1. The problem statement, all variables and given/known data
    Design a combinational circuit that multiplies two numbers together, and outputs the result.

    2. Relevant equations
    The biggest product will be 3 * 3 = 9.

    Four bits to represent the product.

    0: 00
    1: 01
    2: 10
    3: 11

    I need a 4 bit register for the outputs

    3. The attempt at a solution


    The biggest product will be 3 * 3 = 9.
    Four bits to represent the product.
    0: 00
    1: 01
    2: 10
    3: 11

    I need a 4 bit register for the outputs, right?

    How do I start my truth table? like this?

    A B C D | Output | AB | CD

    How will I form the expressions from the truth table?
    I know how to solve with a K-map, but I'm having a hard time visualizing and building it.
     
  2. jcsd
  3. Sep 21, 2015 #2

    berkeman

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    Staff: Mentor

    Welcome to the PF.

    I don't think you need the last part of the above -- what is it meant to represent?

    Just fill out the truth table with the 2x2-bit inputs and the resulting 4-bit output. Then do a K-map for each of the 4 output bits versus the 4 input bits. Can you show us that truth table?

    Hint -- use the [ code ] and [ /code ] tags (without the spaces) around your truth table to enforce uniform spacing of the characters so the columns line up. :smile:
     
  4. Sep 21, 2015 #3
    Okay I uploaded a picture. I put the 1's in the K-map after and now i need to form the expression. I build the circuit from the expression then?
     

    Attached Files:

  5. Sep 21, 2015 #4

    berkeman

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    Staff: Mentor

    That table doesn't make any sense to me.

    The Truth Table for this 2-bit multiplier should have 4 columns of input bits and 4 columns of output bits. The output bits for each row are the binary result of multiplying the two 2-bit input binary numbers.

    Try again? :smile:
     
  6. Sep 21, 2015 #5
    I uploaded another.. I don't understand how to get the highs in the x,y,z outputs though, what am I looking at to form the logic?
     

    Attached Files:

  7. Sep 21, 2015 #6

    berkeman

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    Staff: Mentor

    Much better! :smile:

    So now you design 4 logic circuits, one each for the W, X, Y and Z outputs. The 4 inputs (A, B, C, D) go into each of the combinatorial circuits.

    Use 4 K-maps to design the 4 logic circuits. Can you show us your try at the 4 K-maps?
     
  8. Sep 21, 2015 #7
    Here's a look at my K-Map and expressions. Now I take the expressions and build the circuit in a testing program?
     

    Attached Files:

  9. Sep 21, 2015 #8

    berkeman

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    Staff: Mentor

    Great! I checked the K-maps and they look right for W, X, Y and Z (from top to bottom -- they should be labeled).

    And yes, now just write down the circuits that correspond to those minterms. Good work. :smile:
     
  10. Sep 21, 2015 #9
    Thanks for your help, appreciated greatly! I never turned a big expression like B'CD + A'BD + BCD + ABD + DB into a circuit before. Do I take the expressions for w,x,y,z and put them altogether?
     
  11. Sep 21, 2015 #10

    berkeman

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    Staff: Mentor

    No, you will make 4 separate circuits; one each for the W, X, Y, and Z output bits for the multiplier. You make each circuit with inverters, AND gates and OR gates (that's one way to implement minterms anyway).
     
  12. Sep 21, 2015 #11
    Can you help me set one up, preferably a harder one?

    AC'D+ AB'D + BCD' + A'BC
     
  13. Sep 21, 2015 #12
    Will I have three Or's in that expression?
     
  14. Sep 23, 2015 #13

    berkeman

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    Yes. Sorry for the delay in responding.

    You implement that with inverters, AND gates, and OR gates. For the terms like C', use an inverter to make C' from the C input. For terms like AC'D, use a 3-input AND gate. And then use OR gates to implement the "+" operations.
     
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