DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A
8th Edition
ISBN: 9781260521337
Author: ROSEN
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 12.4, Problem 15E
Find the cells in a K-map for Boolean functions with five variables that correspond to each of these products.
a) x1x2x3x4
b) x1x3x5
c) x2x4
d) x3x4
e)x3
f) x5
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Evaluate |
x + 2x +3
Vx* +x +1
xp-
17) Explain why these two quotients are different. Compute each one.
(x – 2)*
x* - 16
and
X - 2
x- 2
if c(p,s,h) is the cost of buying p bags of chips, s sodas, and h hot dogs, use functional notation to express the cost of buying 2 bags of potato chips, 3 sodas, and 5 hot dogs
Chapter 12 Solutions
DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A
Ch. 12.1 - Prob. 1ECh. 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. 16ECh. 12.1 - Exercises 14-23 deal with the Boolean algebra {0,...Ch. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - Prob. 20ECh. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - Exercises 4-3 deal with the Boolean algebra {0, 1}...Ch. 12.1 - Prob. 24ECh. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 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. 29ECh. 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. 37ECh. 12.1 - Prob. 38ECh. 12.1 - In Exercises 35-42, use the laws in Definition 1...Ch. 12.1 - Prob. 40ECh. 12.1 - Prob. 41ECh. 12.1 - Prob. 42ECh. 12.1 - Prob. 43ECh. 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. 8ECh. 12.2 - Prob. 9ECh. 12.2 - Another way to find a Boolean expression that...Ch. 12.2 - Prob. 11ECh. 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. 15ECh. 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. 1ECh. 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. 7ECh. 12.4 - Prob. 8ECh. 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. 11ECh. 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. 20ECh. 12.4 - Prob. 21ECh. 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. 24ECh. 12.4 - Use the Quine—McCluskey method to simplify the...Ch. 12.4 - Prob. 26ECh. 12.4 - Prob. 27ECh. 12.4 - Prob. 28ECh. 12.4 - Prob. 29ECh. 12.4 - Prob. 30ECh. 12.4 - Prob. 31ECh. 12.4 - Prob. 32ECh. 12.4 - show that products of k literals correspond to...Ch. 12 - Define a Boolean function of degreen.Ch. 12 - Prob. 2RQCh. 12 - Prob. 3RQCh. 12 - Prob. 4RQCh. 12 - Prob. 5RQCh. 12 - Prob. 6RQCh. 12 - Explain how to build a circuit for a light...Ch. 12 - Prob. 8RQCh. 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. 1SECh. 12 - Prob. 2SECh. 12 - Prob. 3SECh. 12 - Prob. 4SECh. 12 - Prob. 5SECh. 12 - Prob. 6SECh. 12 - Prob. 7SECh. 12 - Prob. 8SECh. 12 - Prob. 9SECh. 12 - Prob. 10SECh. 12 - Prob. 11SECh. 12 - Prob. 12SECh. 12 - Prob. 13SECh. 12 - Prob. 14SECh. 12 - Prob. 15SECh. 12 - Prob. 16SECh. 12 - How many of the 16 Boolean functions in two...Ch. 12 - Prob. 18SECh. 12 - Prob. 19SECh. 12 - Design a circuit that determines whether three or...Ch. 12 - Prob. 21SECh. 12 - A Boolean function that can be represented by a...Ch. 12 - Prob. 23SECh. 12 - Prob. 24SECh. 12 - Given the values of two Boolean variablesxandy,...Ch. 12 - Prob. 2CPCh. 12 - Prob. 3CPCh. 12 - Prob. 4CPCh. 12 - Prob. 5CPCh. 12 - Prob. 6CPCh. 12 - Prob. 7CPCh. 12 - Prob. 8CPCh. 12 - Prob. 9CPCh. 12 - Given the table of values of a Boolean function,...Ch. 12 - Prob. 11CPCh. 12 - Prob. 12CPCh. 12 - Prob. 1CAECh. 12 - Prob. 2CAECh. 12 - Prob. 3CAECh. 12 - Prob. 4CAECh. 12 - Prob. 5CAECh. 12 - Prob. 6CAECh. 12 - Prob. 7CAECh. 12 - Describe some of the early machines devised to...Ch. 12 - Explain the difference between combinational...Ch. 12 - Prob. 3WPCh. 12 - Prob. 4WPCh. 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. 11WPCh. 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.Similar questions
- For each pair of integers, express the greatest common divisor of integers as a linear combination of these integers. a) (51, 87) b) (105, 300) c) (981, 1234) d) (34709, 100313)arrow_forwardfx)ン 2 3x -7X ーメ+2X 3x-7X -x²+2X plug-1 in the (x)arrow_forwardLet A- 4-6 Find-3A 4B -3A+48- and B- ::arrow_forward
- a) 2x + 5 > 4x – 3arrow_forwardDefine two operations + and * on A = Z × Z as follows: for (a, b) and (c, d) in A: ɔy (a, b)+(c, d) = (a +c, b+ d) and (a, b) * (c, d) = (ac – bd, bc + ad). For every (a, b), (c, d) and (e, f) in A, show that (a) (a, b)+(c, d) = (c, d)+(a, b) is uncountable (b) (a, b)+((c, d)+(e, ƒ)) = ((a, b)+(c, d))+(e, f) (c) (a, b)*(c, d) = (c, d)*(a, b) (d) (a, b) * ((c, d) * (e, f)) = ((a, b) * (c, d)) * (e, f) (e) (a, b) * ((c, d)+(e, f)) = ((a,b) * (c, d))+((a, b) * (e, f))arrow_forwardDetermine whether the statement, given in inverted commas" is trueor false. If the statement is false, make the necessary change(s) to produce a true statement: "The term x has no coefficient."arrow_forward
- An article in a sociology journal stated that if a particular health-care program for the elderly were initiated, then t years after its start, n thousand elderly people would receive direct benefits, where =글3-612 + 32t [0, 12] n 3= For what value of t does the maximum number receive benefits? O 12 F9 F8 F7 F5 F6 F4 & 7 96arrow_forwardLet Q(x, y) be the statement "x + y = x - y." If the domain for both variables consists of all integers, evaluate 3x3yQ(x, y). O True O Falsearrow_forwardTranslate ap(F(p) ^ B(p)) → ajLj) into English where F(p) is "Printer p is out of service," B(p) is "Printer p is busy," L(j) is “Print job j is lost," and Q(j) is "Print job j is queued." If there is a job that is both queued and lost, then some printer is out of service. B) If there is a printer that is both out of service and busy, then some job has been lost. If every printer is busy, then there is a job in the queue. If every printer is busy and every job is queued, then some job is lost.arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Orthogonality in Inner Product Spaces; Author: Study Force;https://www.youtube.com/watch?v=RzIx_rRo9m0;License: Standard YouTube License, CC-BY
Abstract Algebra: The definition of a Group; Author: Socratica;https://www.youtube.com/watch?v=QudbrUcVPxk;License: Standard Youtube License