Question 1

Prove or disprove that $$x + x y + x y z = x$$ whenever x, y, and z are Boolean variables.

Accepted Answer

When

has the value 1 , then

....

Question 2

Construct a circuit using inverters, OR gates, and AND gates that gives an output of 1 if three people on a committee do not all vote the same.

Accepted Answer

Let $x , y$, and $z$ represent the votes of the three people on the committee with a variable taking the value 1 if the vote is affirmative and the value 0 if the vote is negative. The circuit should produce an output of 1 if and only if not all three of the variables have the same value. The function $f ( x , y , z ) = \overline { ( x y z + \bar { x } \bar { y } \bar { z } ) }$ gives this output. Hence we can use the following circuit.

Question 3

Is the set of operators {+, ·} functionally complete? Justify your answer.

Accepted Answer

The set of operators <img  loading="lazy" src="/assets/images/blured-textbook.svg" class="d-inline m-1" alt="blured image" width="139" height="30"> is not functionall...

Question 4

What is the output of the following circuit?

Accepted Answer

The output of the circuit is $$\bar { x } y + x \bar { z }$$

Question 5

Find the sum-of-products expansion of a Boolean function f(x, y, z) that is 1 if and only if x = y = 1 and z = 0, or x = 0 and y = z = 1, or x = y = 0 and z = 1.

Accepted Answer

The sum-of-products ...

Question 6

Prove or disprove that x y + y = y whenever x and y are Boolean variables.

Accepted Answer

When y = 1 we have x y + y = x...

Question 7

Find a Boolean function f(x, y, z) that has the value 1 if and only if exactly two of x, y, and z have the value 1.

Accepted Answer

We want the sum-of-products ex...

Question 8

How many diﬀerent Boolean functions are there of degree 3?

Accepted Answer

The answer of How many diﬀerent Boolean functions are there...

Question 9

What is the value of the Boolean function $$f ( x , y , z ) = ( \bar { x } + \bar { y } ) z + x y z \text { when } x = 1 , y = 0 \text { and } z = 1 ?$$

Accepted Answer

We have f(1, 0, 1) =...

Question 10

Use a K-map to minimize the sum-of-products expansion x y z + x y z + x y z + x y z.

Accepted Answer

We construct the fol...

Question 11

Use a K-map to minimize the sum-of-products expansion $x y z + x \bar { y } z + \bar { x } \bar { y } z + x \bar { y } \bar { z } + \bar { x } y z + \bar { x } \bar { y } \bar { z }$

Accepted Answer

We construct the following K-map.  This gives us the expansion $$\bar { y } + z$$

Exam 12: Boolean Algebra

Prove or disprove that $x + x y + x y z = x$ whenever x, y, and z are Boolean variables.

Correct Answer
verified
When has the value 1 , then ....
View Answer

Construct a circuit using inverters, OR gates, and AND gates that gives an output of 1 if three people on a committee do not all vote the same.

Is the set of operators {+, ·} functionally complete? Justify your answer.

Correct Answer
verified
The set of operators is not functionall...
View Answer

What is the output of the following circuit?

Correct Answer
verified
The output of the circuit is \[\bar { x } y + x \bar { z }\]

Find the sum-of-products expansion of a Boolean function f(x, y, z) that is 1 if and only if x = y = 1 and z = 0, or x = 0 and y = z = 1, or x = y = 0 and z = 1.

Correct Answer
verified
The sum-of-products ...
View Answer

Prove or disprove that x y + y = y whenever x and y are Boolean variables.

Correct Answer
verified
When y = 1 we have x y + y = x...
View Answer

Find a Boolean function f(x, y, z) that has the value 1 if and only if exactly two of x, y, and z have the value 1.

Correct Answer
verified
We want the sum-of-products ex...
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How many diﬀerent Boolean functions are there of degree 3?

Correct Answer
verified

What is the value of the Boolean function $f ( x , y , z ) = ( \bar { x } + \bar { y } ) z + x y z \text { when } x = 1 , y = 0 \text { and } z = 1 ?$

Correct Answer
verified
We have f(1, 0, 1) =...
View Answer

Use a K-map to minimize the sum-of-products expansion x y z + x y z + x y z + x y z.

Correct Answer
verified
We construct the fol...
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Use a K-map to minimize the sum-of-products expansion $x y z + x \bar { y } z + \bar { x } \bar { y } z + x \bar { y } \bar { z } + \bar { x } y z + \bar { x } \bar { y } \bar { z }$

Correct Answer
verified
We construct the following K-map. 11eb49e0_d240_dc4d_b736_299c373e6c6f_TB6843_00 This gives us the expansion \[\bar { y } + z\]

Exam 12: Boolean Algebra

Prove or disprove that x+xy+xyz=xx + x y + x y z = xx+xy+xyz=x whenever x, y, and z are Boolean variables.

Correct AnswerverifiedWhen has the value 1 , then ....View AnswerShow Answer

Construct a circuit using inverters, OR gates, and AND gates that gives an output of 1 if three people on a committee do not all vote the same.

Is the set of operators {+, ·} functionally complete? Justify your answer.

Correct AnswerverifiedThe set of operators is not functionall...View AnswerShow Answer

What is the output of the following circuit?

Correct AnswerverifiedThe output of the circuit is \[\bar { x } y + x \bar { z }\]

Find the sum-of-products expansion of a Boolean function f(x, y, z) that is 1 if and only if x = y = 1 and z = 0, or x = 0 and y = z = 1, or x = y = 0 and z = 1.

Correct AnswerverifiedThe sum-of-products ...View AnswerShow Answer

Prove or disprove that x y + y = y whenever x and y are Boolean variables.

Correct AnswerverifiedWhen y = 1 we have x y + y = x...View AnswerShow Answer

Find a Boolean function f(x, y, z) that has the value 1 if and only if exactly two of x, y, and z have the value 1.

Correct AnswerverifiedWe want the sum-of-products ex...View AnswerShow Answer

How many diﬀerent Boolean functions are there of degree 3?

Correct AnswerverifiedShow Answer

What is the value of the Boolean function f(x,y,z)=(xˉ+yˉ)z+xyz when x=1,y=0 and z=1?f ( x , y , z ) = ( \bar { x } + \bar { y } ) z + x y z \text { when } x = 1 , y = 0 \text { and } z = 1 ?f(x,y,z)=(xˉ+yˉ​)z+xyz when x=1,y=0 and z=1?

Correct AnswerverifiedWe have f(1, 0, 1) =...View AnswerShow Answer

Use a K-map to minimize the sum-of-products expansion x y z + x y z + x y z + x y z.

Correct AnswerverifiedWe construct the fol...View AnswerShow Answer

Use a K-map to minimize the sum-of-products expansion xyz+xyˉz+xˉyˉz+xyˉzˉ+xˉyz+xˉyˉzˉx y z + x \bar { y } z + \bar { x } \bar { y } z + x \bar { y } \bar { z } + \bar { x } y z + \bar { x } \bar { y } \bar { z }xyz+xyˉ​z+xˉyˉ​z+xyˉ​zˉ+xˉyz+xˉyˉ​zˉ

Correct AnswerverifiedWe construct the following K-map. 11eb49e0_d240_dc4d_b736_299c373e6c6f_TB6843_00 This gives us the expansion \[\bar { y } + z\]

Prove or disprove that $x + x y + x y z = x$ whenever x, y, and z are Boolean variables.

Correct Answer
verified
When has the value 1 , then ....
View Answer

Correct Answer
verified
The set of operators is not functionall...
View Answer

Correct Answer
verified
The output of the circuit is \[\bar { x } y + x \bar { z }\]

Correct Answer
verified
The sum-of-products ...
View Answer

Correct Answer
verified
When y = 1 we have x y + y = x...
View Answer

Correct Answer
verified
We want the sum-of-products ex...
View Answer

Correct Answer
verified

What is the value of the Boolean function $f ( x , y , z ) = ( \bar { x } + \bar { y } ) z + x y z \text { when } x = 1 , y = 0 \text { and } z = 1 ?$

Correct Answer
verified
We have f(1, 0, 1) =...
View Answer

Correct Answer
verified
We construct the fol...
View Answer

Use a K-map to minimize the sum-of-products expansion $x y z + x \bar { y } z + \bar { x } \bar { y } z + x \bar { y } \bar { z } + \bar { x } y z + \bar { x } \bar { y } \bar { z }$

Correct Answer
verified
We construct the following K-map. 11eb49e0_d240_dc4d_b736_299c373e6c6f_TB6843_00 This gives us the expansion \[\bar { y } + z\]