# Truth table for the Boolean equation

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

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#### Solution Preview

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.