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Boolean Algebra
67 questions By Tony R. Kuphaldt
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Question 64 of 67
Simplify this logic gate circuit, which uses nothing but NOR gates to accomplish a certain logic function:
Reveal answer
Notes:This question stands as an example of how NOR gates may be used to construct different types of logic functions. In fact, with a sufficient quantity of NOR gates, any logic function may be built. This is why NOR gates are said to be “universal.”
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Question 65 of 67
Sum-of-Products (SOP) expressions may be implemented by a combination of AND and OR gates, as such:
Use DeMorgan’s Theorem to prove that this NAND gate circuit performs the exact same function:
Reveal answerI’ll leave the proof up to you!
Notes:This is a very practical application of DeMorgan’s Theorem. Being able to use all NAND gates to implement an SOP function is a bonus over having to use separate AND and OR integrated circuit packages (one IC instead of two in this particular case).
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Question 66 of 67
Write the Boolean expression for this logic gate circuit, then reduce that expression to its simplest form using any applicable Boolean laws and theorems. Finally, draw a new gate circuit diagram based on the simplified Boolean expression that performs the exact same logic function.
Reveal answerOriginal Boolean expression: \(\overline{AB} \ \overline{BC}\)
Reduced gate circuit:
Notes:This particular circuit is an example of how a combinational logic function may be implemented using nothing but NAND gates.
Question 29, answer 3 has a typo - should be A*B + !(D)*E not A*B+!(D*E)