 2.4.1: Give the output signals for the circuits in 14 if the input signals...
 2.4.2: Give the output signals for the circuits in 14 if the input signals...
 2.4.3: Give the output signals for the circuits in 14 if the input signals...
 2.4.4: Give the output signals for the circuits in 14 if the input signals...
 2.4.5: In 58, write an input/output table for the circuit in the reference...
 2.4.6: In 58, write an input/output table for the circuit in the reference...
 2.4.7: In 58, write an input/output table for the circuit in the reference...
 2.4.8: In 58, write an input/output table for the circuit in the reference...
 2.4.9: In 912, find the Boolean expression that corresponds to the circuit...
 2.4.10: In 912, find the Boolean expression that corresponds to the circuit...
 2.4.11: In 912, find the Boolean expression that corresponds to the circuit...
 2.4.12: In 912, find the Boolean expression that corresponds to the circuit...
 2.4.13: Construct circuits for the Boolean expressions in 1317
 2.4.14: Construct circuits for the Boolean expressions in 1317
 2.4.15: Construct circuits for the Boolean expressions in 1317
 2.4.16: Construct circuits for the Boolean expressions in 1317
 2.4.17: Construct circuits for the Boolean expressions in 1317
 2.4.18: For each of the tables in 1821, construct (a) a Boolean expression ...
 2.4.19: For each of the tables in 1821, construct (a) a Boolean expression ...
 2.4.20: For each of the tables in 1821, construct (a) a Boolean expression ...
 2.4.21: For each of the tables in 1821, construct (a) a Boolean expression ...
 2.4.22: Design a circuit to take input signals P, Q, and R and output a 1 i...
 2.4.23: Design a circuit to take input signals P, Q, and R and output a 1 i...
 2.4.24: The lights in a classroom are controlled by two switches: one at th...
 2.4.25: An alarm system has three different control panels in three differe...
 2.4.26: Use the properties listed in Theorem 2.1.1 to show that each pair o...
 2.4.27: Use the properties listed in Theorem 2.1.1 to show that each pair o...
 2.4.28: Use the properties listed in Theorem 2.1.1 to show that each pair o...
 2.4.29: Use the properties listed in Theorem 2.1.1 to show that each pair o...
 2.4.30: For the circuits corresponding to the Boolean expressions in each o...
 2.4.31: For the circuits corresponding to the Boolean expressions in each o...
 2.4.32: The Boolean expression for the circuit in Example 2.4.5 is (P Q R) ...
 2.4.33: a. Show that for the Sheffer stroke , P Q (P  Q)(P  Q). b. Use ...
 2.4.34: Show that the following logical equivalences hold for the Peirce ar...
Solutions for Chapter 2.4: Application: Digital Logic Circuits
Full solutions for Discrete Mathematics with Applications  4th Edition
ISBN: 9780495391326
Solutions for Chapter 2.4: Application: Digital Logic Circuits
Get Full SolutionsDiscrete Mathematics with Applications was written by and is associated to the ISBN: 9780495391326. This textbook survival guide was created for the textbook: Discrete Mathematics with Applications , edition: 4. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2.4: Application: Digital Logic Circuits includes 34 full stepbystep solutions. Since 34 problems in chapter 2.4: Application: Digital Logic Circuits have been answered, more than 51868 students have viewed full stepbystep solutions from this chapter.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Column space C (A) =
space of all combinations of the columns of A.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.