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    Truth table for the Boolean equation

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    Please assist with the attached 5 problems. I've answered 1 and 3 but are not certain if they are correct. If they are not correct can you please show how to solve these problems.

    1. Construct a truth table for the Boolean equation:
    M = A'B C' + A'B C + A B'C + A B C

    A B C M
    0 0 0 0
    0 0 1 0
    0 1 0 1
    0 1 1 1
    1 0 0 0
    1 0 1 1
    1 1 0 0
    1 1 1 1

    1*0*1 + 1*0*0 + 0*1*0 + 0*0*0
    0 + 0 + 0 + 0 = 0
    1*0*0 + 1*0*1 + 0*1*1 + 0*0*1
    0 + 0 + 0 + 0 = 0
    1*1*1 + 1*1*0 + 0*0*0 + 0*1*0
    1 + 0 + 0 + 0 = 1
    1*1*0 + 1*1*1 + 0*0*1 + 0*1*1
    0 + 1 + 0 + 0 = 0
    0*0*1 + 0*0*0 + 1*1*0 + 1*0*0
    0 + 0 + 0 + 0 = 0
    0*0*0 + 0*0*1 + 1*1*1 + 1*0*1
    0 + 0 + 1 + 0 = 1
    0*1*1 + 0*1*0 + 1*0*0 + 1*1*0
    0 + 0 + 0 + 0 = 0
    0*1*0 + 0*1*1 + 1*0*1 + 1*1*1
    0 + 0 + 0 + 1 = 1

    2. Draw a simple NOT, AND, OR circuit in sum of products (SOP) form that represents the equation above.

    3. The truth table for a Boolean expression is shown below. Write the Boolean expression on SOP form

    x y z F
    0 0 0 1
    0 0 1 0
    0 1 0 0
    0 1 1 1
    1 0 0 1
    1 0 1 1
    1 1 0 0
    1 1 1 1

    F(x,y,z)=x'y'z'+x'yz+xy'z'+xy'z+xyz

    4. Find the truth table that describes the following circuit:

    5. Describe the function of a decoder circuit;

    identify the types and quantity of gates needed to implement a 3-to-8 decoder;

    either create (or give the location in the text) of a logic diagram of a decoder circuit

    © BrainMass Inc. brainmass.com October 10, 2019, 8:23 am ad1c9bdddf
    https://brainmass.com/math/logic/truth-table-boolean-equation-622803

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    Hi,

    Please find detailed solutions attached herewith.
    I hope it will help you. I will be happy to assist you in future.

    Thanks

    1. Construct a truth table for the Boolean equation:
    M = A'B C' + A'B C + A B'C + A B C

    A B C M
    0 0 0 0
    0 0 1 0
    0 1 0 1
    0 1 1 1
    1 0 0 0
    1 0 1 1
    1 1 0 0
    1 1 1 1

    1*0*1 + 1*0*0 + 0*1*0 + 0*0*0
    0 + 0 + 0 + 0 = 0
    1*0*0 + 1*0*1 + 0*1*1 + 0*0*1
    0 + 0 + 0 ...

    Solution Summary

    This posting explains how to construct a truth table for the Boolean equation and how to a simple NOT, AND, OR circuit.

    $2.19