Assignment:
Question 1. Construct a truth table for the Boolean equation:
M = A’B C’ + A’B C + A B’C + A B C
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A
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B
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C
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M
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0
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0
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0
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0
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0
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0
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1
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0
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0
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1
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0
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1
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0
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1
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1
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1
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1
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0
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0
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0
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1
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0
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1
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1
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1
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1
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0
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0
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1
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1
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1
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1
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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
Question 2. Draw a simple NOT, AND, OR circuit in sum of products (SOP) form that represents the equation above.
Question 3. The truth table for a Boolean expression is shown below. Write the Boolean expression on SOP form
F(x,y,z)=x’y’z’+x’yz+xy’z’+xy’z+xyz
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x
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y
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z
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F
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0
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0
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0
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1
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0
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0
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1
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0
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0
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1
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0
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0
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0
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1
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1
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1
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1
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0
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0
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1
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1
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0
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1
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1
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1
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1
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0
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0
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1
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1
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1
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1
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Question 4. Find the truth table that describes the following circuit:
Question 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.
Provide complete and step by step solution for the question and show calculations and use formulas.