DISCRETE MATHEMATICS LOOSELEAF
8th Edition
ISBN: 9781264309689
Author: ROSEN
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 12.3, Problem 12E
Use the circuits from Exercises 10 and 11 to find the difference of two four-bit integers, where the first integer is greater than the second integer.
10.Construct a circuit for a half subtractor using AND gates, OR gates, and inverters. A half subtractor has two bits as input and produces as output a difference bit and a borrow.
11. Construct a circuit for a full subtractor using ND gates. OR gates, and inverters. A full subtractor has two bits and a borrow as input, and produces as output a difference bit and a borrow.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
i need help please and thank you
The parameters of an RLC circuit with an input voltage of E(t) are given.
R=202, L=10 H, C = 0.01 F, E(t) = 200 cos 4t V
Using the initial conditions I(0) = 0 and Q(0) = 4, plot both the steady periodic current I sp(t) and the total current I(t) = Isp (t) + Itr(t).
Find the steady periodic solution Xsp (t) = C cos (@t - α) of the given equation mx" + cx' + kx = F(t) with periodic forcing function F(t) of frequency w. Then graph xsp (t) together with (for
comparison) the adjusted function F₁ (t) :
F(t)
mo
x'' + 4x' + 43x = 9 cos 6t
Chapter 12 Solutions
DISCRETE MATHEMATICS LOOSELEAF
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...
Additional Math Textbook Solutions
Find more solutions based on key concepts
1. How much money is Joe earning when he’s 30?
Pathways To Math Literacy (looseleaf)
In Exercises 5-36, express all probabilities as fractions.
23. Combination Lock The typical combination lock us...
Elementary Statistics
In Exercises 9-20, use the data in the following table, which lists drive-thru order accuracy at popular fast f...
Elementary Statistics (13th Edition)
Silvia wants to mix a 40% apple juice drink with pure apple juice to make 2 L of a juice drink that is 80% appl...
Beginning and Intermediate Algebra
For each hour of class time, how many hours outside of class are recommended for studying and doing homework?
Elementary Algebra For College Students (10th Edition)
For Problems 23-28, write in simpler form, as in Example 4. logbFG
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
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
- Can you please solve this and show steps of dimensional analysis. Thank you. The values for A-E are written above. Refer to top paragraph for contentarrow_forward2. (15 pts) Write the Maclaurin series for the function f(x) = sinx. Use it to write the Maclaurin series for g(x) = sin. Express find as a series. Write it in sigma notation as well.arrow_forward- Let f (x) = √x sin( X/12), × 0. D x = ○ Show that f is continuous at x=0. 3 Let f(x) = ( + sin(x2) x +0 ' Lo. X = 6 Show that f is discontinuous at x=0. 9 Let a, b & R, acb. Let f be a real-valued function on [a,b]. 10 (a) Define what we mean by "f is bounded." (b) Assume is bounded and let m = M = inf {f(x): xe [a,b]} sup {f(x): x = [a,b]}. Prove that there exist Xo, & [a,b] such that Хо f(xo) Im and f(x) = M. = น Prove the Intermediate Value theorem for f as in ⑦ that for each yε [m,M] there exists. xe [a, b] such that f(x) = y. Conclude that f([a,b]) = [m, M].arrow_forward
- A mass weighing 80 lbs (mass m = 2.5 in fps) is attached to the end of a spring that is stretched 8 in. by a force of 80 lbs. A force Fo cos wt acts on the mass. At what frequency (in hertz) will resonance oscillations occur? Neglect damping.arrow_forward①(a) Let rεR, o≤r<1. Prove directly from defintions. 2 = r ++²+3+... that the series r = 1 is convergent with sum 1-2 +p+.... (b) Prove that the harmonic series 2 ½ is divergent. นะเ n ② (a) Define what is meant by the following: (1) the sequence (an) is convergent. (ii) the sequence (an) is Cauchy. (ii) the sequence (an) is bounded. (b) Prove directly from definitions that a Cauchy Sequence is bounded. ③ (a) Prove diredly from definitions that if a Cauchy Sequence (an) has a convergent subsequence then (an) is convergent. (6) Use the results of 2(b) and 3(a) to deduce that a Counchy sequence is convergent. You may assume the Bolzano- Weierstrass Theorem.arrow_forwardExpress the solution of the given initial value problem as a sum of two oscillations. Primes denote derivatives with respect to time t. Graph the solution function x(t) in such a way that you can identify and label its period. x" + 49x=26 cos 6t; x(0) = x'(0) = 0arrow_forward
- If u = (2, 3, 1) and v = (-3, 2,0), find a. u.v b. The angle between u and varrow_forwardFind the nullity of T, if a. T: R5 R2 and rank(T) = 3. b. T: P3 P4 and rank(T) = 2. c. T: M3x1M1×3 and rank(T) = 0. d. T R R and rank (T) = 1.arrow_forwardThis problem deals with the RL circuit shown here, a series circuit containing an inductor, a resistor, and a source of electromotive force (emf), but no capacitor. The linear first-order differential equation governing the current in this circuit is given by the following. LI' + RI = E(t) Suppose that L = 5 H, R = 202, and the source E of emf is an alternating-current generator that supplies a voltage of E(t) = 100 cos (40t) V. Suppose that the switch is initially in position 2, but is thrown to position 1 at time t = 0 so that I(0) = 0. Determine the subsequent inductor current, I(t). E Switch 2 R wwarrow_forward
- I would like to get help to know how to make a report of the multiple regression analysis I performed about 30 employees salaries. it should include a description of the predictice model, pre-analysis, regression analysis, interpretation of the relevant findings and a conclusion with recommendations. thank youarrow_forwardtion: Solve the following systems using Gaussian Elimination with Backward substitu- x- 2y+32=9 -x+3y =-4 2x-5y+5z = 17arrow_forwardProve the following inequalities: Ꮖ 1. x - x2 0 2 2. sin x > x - 3³ for x > 0 6arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
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
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher: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
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Finite State Machine (Finite Automata); Author: Neso Academy;https://www.youtube.com/watch?v=Qa6csfkK7_I;License: Standard YouTube License, CC-BY
Finite State Machine (Prerequisites); Author: Neso Academy;https://www.youtube.com/watch?v=TpIBUeyOuv8;License: Standard YouTube License, CC-BY