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Boolean Algebra
67 questions By Tony R. Kuphaldt
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Question 7 of 67
Surveying the rules for Boolean multiplication, the 0 and 1 values seem to resemble the truth table of a very common logic gate. Which type of gate is this, and what does this suggest about the relationship between Boolean multiplication and logic circuits?
Rules for Boolean multiplication: $$0 \ x \ 0=0$$
$$0 \ x \ 1=0$$
$$1 \ x \ 0=0$$
$$1 \ x \ 1 =1$$Reveal answerThis set of Boolean expressions resembles the truth table for an AND logic gate circuit, suggesting that Boolean multiplication may symbolize the logical AND function.
Notes:Students need to be able to readily associate fundamental Boolean operations with logic circuits. If they can see the relationship between the “strange” rules of Boolean arithmetic and something they are already familiar with (i.e. truth tables), the association is made much easier.
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Question 8 of 67
What is the complement of a Boolean number? How do we represent the complement of a Boolean variable, and what logic circuit function performs the complementation function?
Reveal answerA Boolean “complement” is the opposite value of a given number. This is represented either by overbars or prime marks next to the variable (i.e. the complement of A may be written as either \(\overline{A}\) or A′):
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Notes:Students need to be able to readily associate fundamental Boolean operations with logic circuits. If they can see the relationship between the “strange” rules of Boolean arithmetic and something they are already familiar with (i.e. truth tables), the association is made much easier.
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Question 9 of 67
There are three fundamental operations in Boolean algebra: addition, multiplication, and inversion. Each of these operations has an equivalent logic gate function and an equivalent relay circuit configuration. Draw the corresponding gate and ladder logic diagrams for each:
Reveal answer
Notes:These three equivalencies will be vital for students to master as they study combinational logic circuits and complex relay logic circuits!
Question 29, answer 3 has a typo - should be A*B + !(D)*E not A*B+!(D*E)