Q6: PoS & SoP
Time Estimate15-30 minutes Grade Impact0.5% DueSep 21 @ 12pm
Objective
Reinforce an understanding of PoS and SoP.
Additional Materials & Formats
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Free Response Questions
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What is the purpose of minterms and maxterms?
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How does the Principle of Duality apply to the relationship between SoP and PoS?
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Do you personally prefer PoS or SoP? Why?
Multiple Choice Questions
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Which statement best defines a minterm for n Boolean variables?
- A product (AND) term that is true for exactly one input combination.
- A sum (OR) term that is true for exactly one input combination.
- Any product term with at least one complemented variable.
- Any canonical PoS clause.
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For four variables, how many distinct minterms exist?
- 8
- 16
- 15
- 7
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A canonical Product of Sums (PoS) form is composed of:
- OR clauses (each a maxterm) multiplied (ANDed) together, each clause false for exactly one input row.
- AND clauses (each a minterm) added (ORed) together, each clause true for exactly one input row.
- XOR clauses combined to cover all 1 outputs.
- NAND gates only.
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If $F = \sum m(1,3,4)$, which of the following is an equivalent statement in terms of maxterms?
- $F = \Pi M(0,2,5,6,7) $
- $F = \Pi M(0,2,5,6) $
- $F = \Pi M(0,2,5,6,7,…)$ (incomplete)
- $F = \sum m(0,2,5,6) $
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Which of the following is true about maxterms?
- A maxterm is an OR clause that evaluates to 0 for exactly one combination of inputs.
- A maxterm is an AND clause that evaluates to 1 for exactly one combination of inputs.
- Maxterms are used only in SoP representations.
- A single maxterm can represent multiple input rows where the function is 0.
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Which of the following is true about minterms?
- A minterm is an AND clause that evaluates to 1 for exactly one combination of inputs.
- A minterm is an OR clause that evaluates to 0 for exactly one combination of inputs.
- Minterms are used to build canonical PoS expressions.
- A single minterm can represent multiple input rows where the function is 1.
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Which of the following is a minterm for variables $x_1, x_2, x_3$ when $x_1=1,\ x_2=0,\ x_3=1$?
- $x_1\overline{x_2}x_3$
- $\overline{x_1}x_2\overline{x_3}$
- $x_1 + \overline{x_2} + x_3$
- $\overline{x_1}+x_2+\overline{x_3}$