Explanation Given: A function with two variable. Concept used: k − Map for a Boolean function with n variables has 2 n cells where n is equal to number of variables. Calculation: The min term x ¯ y has two variables we consider the k − map of two variables having 2 2 blocks i.e. 4 cells. y y ¯ x To determine (b) The min terms represented by cells adjacent to x ¯ y .

Discrete Mathematics And Its Applications

8th Edition

ISBN: 9781260091991

Author: NA

Publisher: Mc graw hill

See similar textbooks

Concept explainers

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Chapter 12.4, Problem 1E

To determine

(a)

To draw a k− map for function in two variables and put 1 in cell representing x¯y.

To determine

(b)

The min terms represented by cells adjacent to x¯y.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.3, Problem 20E

Chapter 12.4, Problem 2E

Students have asked these similar questions

Answer questions 8.3.3 and 8.3.4 respectively 8.3.4 .WP An article in Medicine and Science in Sports and Exercise [“Electrostimulation Training Effects on the Physical Performance of Ice Hockey Players” (2005, Vol. 37, pp. 455–460)] considered the use of electromyostimulation (EMS) as a method to train healthy skeletal muscle. EMS sessions consisted of 30 contractions (4-second duration, 85 Hz) and were carried out three times per week for 3 weeks on 17 ice hockey players. The 10-meter skating performance test showed a standard deviation of 0.09 seconds. Construct a 95% confidence interval of the standard deviation of the skating performance test.

8.6.7 Consider the tire-testing data in Exercise 8.2.3. Compute a 95% tolerance interval on the life of the tires that has confidence level 95%. Compare the length of the tolerance interval with the length of the 95% CI on the population mean. Which interval is shorter? Discuss the difference in interpretation of these two intervals.

8.6.2 Consider the natural frequency of beams described in Exercise 8.2.8. Compute a 90% prediction interval on the diameter of the natural frequency of the next beam of this type that will be tested. Compare the length of the prediction interval with the length of the 90% CI on the population mean. 8.6.3 Consider the television tube brightness test described in Exercise 8.2.7. Compute a 99% prediction interval on the brightness of the next tube tested. Compare the length of the prediction interval with the length of the 99% CI on the population mean.

Chapter 12 Solutions

Discrete Mathematics And Its Applications

Ch. 12.1 - Prob. 1E Ch. 12.1 - Find the values, if any, of the Boolean...Ch. 12.1 - a) Show that(1.1)+(0.1+0)=1 . b) Translate the...Ch. 12.1 - a) Show that(10)+(10)=1 . b) Translate the...Ch. 12.1 - Use a table to express the values of each of these...Ch. 12.1 - Use a table to express the values of each of these...Ch. 12.1 - Use a 3-cubeQ3to represent each of the Boolean...Ch. 12.1 - Use a 3-cubeQ3to represent each of the Boolean...Ch. 12.1 - What values of the Boolean...Ch. 12.1 - How many different Boolean functions are there of...

Ch. 12.1 - Prove the absorption lawx+xy=x using the other...Ch. 12.1 - Show thatF(x,y,z)=xy+xz+yz has the value 1 if and...Ch. 12.1 - Show thatxy+yz+xz=xy+yz+xz .Ch. 12.1 - 3Exercises 14-23 deal the Boolean algebra {0, 1}...Ch. 12.1 - Exercises 14-23 deal with the Boolean algebra {0,...Ch. 12.1 - Prob. 16E Ch. 12.1 - Exercises 14-23 deal with the Boolean algebra {0,...Ch. 12.1 - Prob. 18E Ch. 12.1 - Prob. 19E Ch. 12.1 - Prob. 20E Ch. 12.1 - Prob. 21E Ch. 12.1 - Prob. 22E Ch. 12.1 - Exercises 4-3 deal with the Boolean algebra {0, 1}...Ch. 12.1 - Prob. 24E Ch. 12.1 - Prob. 25E Ch. 12.1 - Prob. 26E Ch. 12.1 - Prove or disprove these equalities. a)x(yz)=(xy)z...Ch. 12.1 - Find the duals of these Boolean expressions. a)x+y...Ch. 12.1 - Prob. 29E Ch. 12.1 - Show that ifFandGare Boolean functions represented...Ch. 12.1 - How many different Boolean functionsF(x,y,z) are...Ch. 12.1 - How many different Boolean functionsF(x,y,z) are...Ch. 12.1 - Show that you obtain De Morgan’s laws for...Ch. 12.1 - Show that you obtain the ab,sorption laws for...Ch. 12.1 - In Exercises 35-42, use the laws in Definition 1...Ch. 12.1 - In Exercises 35-42, use the laws in Definition to...Ch. 12.1 - Prob. 37E Ch. 12.1 - Prob. 38E Ch. 12.1 - In Exercises 35-42, use the laws in Definition 1...Ch. 12.1 - Prob. 40E Ch. 12.1 - Prob. 41E Ch. 12.1 - Prob. 42E Ch. 12.1 - Prob. 43E Ch. 12.2 - Find a Boolean product of the Boolean...Ch. 12.2 - Find the sum of products expansions of these...Ch. 12.2 - Find the sum-of-products expansions of these...Ch. 12.2 - Find the sum-of-products expansions of the Boolean...Ch. 12.2 - Find the sum-of -products expansion of the Boolean...Ch. 12.2 - Find the sum-of-products expansion of the Boolean...Ch. 12.2 - Another way to find a Boolean expression that...Ch. 12.2 - Prob. 8E Ch. 12.2 - Prob. 9E Ch. 12.2 - Another way to find a Boolean expression that...Ch. 12.2 - Prob. 11E Ch. 12.2 - Express each of these Boolean functions using the...Ch. 12.2 - Express each of the Boolean functions in...Ch. 12.2 - Show that a)x=xx . b)xy=(xy)(xy) . c)x+y=(xx)(yy)...Ch. 12.2 - Prob. 15E Ch. 12.2 - Show that{} is functionally complete using...Ch. 12.2 - Express each of the Boolean functions in Exercise...Ch. 12.2 - Express each of the Boolean functions in Exercise...Ch. 12.2 - Show that the set of operators{+,} is not...Ch. 12.2 - Are these sets of operators functionally complete?...Ch. 12.3 - In Exercises 1—5 find the output of the given...Ch. 12.3 - In Exercises 1—5 find the output of the given...Ch. 12.3 - In Exercises 1—5 find the output of the given...Ch. 12.3 - In Exercises 1—5 find the output of the given...Ch. 12.3 - In Exercises 1—5 find the output of the given...Ch. 12.3 - Construct circuits from inverters, AND gates, and...Ch. 12.3 - Design a circuit that implements majority voting...Ch. 12.3 - Design a circuit for a light fixture controlled by...Ch. 12.3 - Show how the sum of two five-bit integers can be...Ch. 12.3 - Construct a circuit for a half subtractor using...Ch. 12.3 - Construct a circuit for a full subtractor using...Ch. 12.3 - Use the circuits from Exercises 10 and 11 to find...Ch. 12.3 - Construct a circuit that compares the two-bit...Ch. 12.3 - Construct a circuit that computes the product of...Ch. 12.3 - Use NAND gates to construct circuits with these...Ch. 12.3 - Use NOR gates to construct circuits for the...Ch. 12.3 - Construct a half adder using NAND gates.Ch. 12.3 - Construct a half adder using NOR gates.Ch. 12.3 - Construct a multiplexer using AND gates, OR gates,...Ch. 12.3 - Find the depth of a) the circuit constructed in...Ch. 12.4 - Prob. 1E Ch. 12.4 - Find the sum-of-products expansions represented by...Ch. 12.4 - Draw the K-maps of these sum-of-products...Ch. 12.4 - Use a K-map to find a minimal expansion as a...Ch. 12.4 - a) Draw a K-map for a function in three variables....Ch. 12.4 - Use K-maps to find simpler circuits with the same...Ch. 12.4 - Prob. 7E Ch. 12.4 - Prob. 8E Ch. 12.4 - Construct a K-map for F(x,y,z) =xz + yz+y z. Use...Ch. 12.4 - Draw the 3-cube Q3 and label each vertex with the...Ch. 12.4 - Prob. 11E Ch. 12.4 - Use a K-map to find a minimal expansion as a...Ch. 12.4 - a) Draw a K-map for a function in four variables....Ch. 12.4 - Use a K-map to find a minimal expansion as a...Ch. 12.4 - Find the cells in a K-map for Boolean functions...Ch. 12.4 - How many cells in a K-map for Boolean functions...Ch. 12.4 - a) How many cells does a K-map in six variables...Ch. 12.4 - Show that cells in a K-map for Boolean functions...Ch. 12.4 - Which rows and which columns of a 4 x 16 map for...Ch. 12.4 - Prob. 20E Ch. 12.4 - Prob. 21E Ch. 12.4 - Use the Quine-McCluskey method to simplify the...Ch. 12.4 - Use the Quine—McCluskey method to simp1i’ the...Ch. 12.4 - Prob. 24E Ch. 12.4 - Use the Quine—McCluskey method to simplify the...Ch. 12.4 - Prob. 26E Ch. 12.4 - Prob. 27E Ch. 12.4 - Prob. 28E Ch. 12.4 - Prob. 29E Ch. 12.4 - Prob. 30E Ch. 12.4 - Prob. 31E Ch. 12.4 - Prob. 32E Ch. 12.4 - show that products of k literals correspond to...Ch. 12 - Define a Boolean function of degreen.Ch. 12 - Prob. 2RQ Ch. 12 - Prob. 3RQ Ch. 12 - Prob. 4RQ Ch. 12 - Prob. 5RQ Ch. 12 - Prob. 6RQ Ch. 12 - Explain how to build a circuit for a light...Ch. 12 - Prob. 8RQ Ch. 12 - Is there a single type of logic gate that can be...Ch. 12 - a) Explain how K-maps can be used to simplify...Ch. 12 - a) Explain how K-maps can be used to simplify...Ch. 12 - a) What is a don’t care condition? b) Explain how...Ch. 12 - a) Explain how to use the Quine-McCluskev method...Ch. 12 - Prob. 1SE Ch. 12 - Prob. 2SE Ch. 12 - Prob. 3SE Ch. 12 - Prob. 4SE Ch. 12 - Prob. 5SE Ch. 12 - Prob. 6SE Ch. 12 - Prob. 7SE Ch. 12 - Prob. 8SE Ch. 12 - Prob. 9SE Ch. 12 - Prob. 10SE Ch. 12 - Prob. 11SE Ch. 12 - Prob. 12SE Ch. 12 - Prob. 13SE Ch. 12 - Prob. 14SE Ch. 12 - Prob. 15SE Ch. 12 - Prob. 16SE Ch. 12 - How many of the 16 Boolean functions in two...Ch. 12 - Prob. 18SE Ch. 12 - Prob. 19SE Ch. 12 - Design a circuit that determines whether three or...Ch. 12 - Prob. 21SE Ch. 12 - A Boolean function that can be represented by a...Ch. 12 - Prob. 23SE Ch. 12 - Prob. 24SE Ch. 12 - Given the values of two Boolean variablesxandy,...Ch. 12 - Prob. 2CP Ch. 12 - Prob. 3CP Ch. 12 - Prob. 4CP Ch. 12 - Prob. 5CP Ch. 12 - Prob. 6CP Ch. 12 - Prob. 7CP Ch. 12 - Prob. 8CP Ch. 12 - Prob. 9CP Ch. 12 - Given the table of values of a Boolean function,...Ch. 12 - Prob. 11CP Ch. 12 - Prob. 12CP Ch. 12 - Prob. 1CAE Ch. 12 - Prob. 2CAE Ch. 12 - Prob. 3CAE Ch. 12 - Prob. 4CAE Ch. 12 - Prob. 5CAE Ch. 12 - Prob. 6CAE Ch. 12 - Prob. 7CAE Ch. 12 - Describe some of the early machines devised to...Ch. 12 - Explain the difference between combinational...Ch. 12 - Prob. 3WP Ch. 12 - Prob. 4WP Ch. 12 - Find out how logic gates are physically...Ch. 12 - Explain howdependency notationcan be used to...Ch. 12 - Describe how multiplexers are used to build...Ch. 12 - Explain the advantages of using threshold gates to...Ch. 12 - Describe the concept ofhazard-free switching...Ch. 12 - Explain how to use K-maps to minimize functions of...Ch. 12 - Prob. 11WP Ch. 12 - Describe what is meant by the functional...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

(a) To draw a k − map for function in two variables and put 1 in cell representing x ¯ y .

Solution Summary: The author calculates the k- map for a Boolean function with n variables.

Concept explainers

(a)

To draw a k− map for function in two variables and put 1 in cell representing x¯y.

(b)

The min terms represented by cells adjacent to x¯y.

Want to see the full answer?

Chapter 12 Solutions

(a) To draw a k − map for function in two variables and put 1 in cell representing x ¯ y .

Solution Summary: The author calculates the k- map for a Boolean function with n variables.

Concept explainers

(a) To draw a k− map for function in two variables and put 1 in cell representing x¯y.

(b) The min terms represented by cells adjacent to x¯y.

Want to see the full answer?

Chapter 12 Solutions

(a)

To draw a k− map for function in two variables and put 1 in cell representing x¯y.

(b)

The min terms represented by cells adjacent to x¯y.