 11.4.11.4.1: a) Draw a Kmap for a function in two variables and put a 1 in the ...
 11.4.11.4.2: Find the sumofproducts expansions represented by each of these K...
 11.4.11.4.3: Draw the Kmaps of these sumofproducts expansions in two variable...
 11.4.11.4.4: Use a Kmap to find a minimal expansion as a Boolean sum of Boolean...
 11.4.11.4.5: a) Draw a Kmap for a function in three variables. Put a 1 in the c...
 11.4.11.4.6: Use Kmaps to find simpler circuits with the same output as each of...
 11.4.11.4.7: Draw the Kmaps of these sumofproducts expansions in three variab...
 11.4.11.4.8: Construct a Kmap for F(x, y, z) = xz + yz + xyz. Use this Kmap to...
 11.4.11.4.9: Construct a Kmap for F(x, y, z) = xz + xyz + yz. Use this Kmap to...
 11.4.11.4.10: Draw the 3cube Q3 and label each vertex with the minterm in the Bo...
 11.4.11.4.11: Draw the 4cube Q4 and label each vertex with the minterm in the Bo...
 11.4.11.4.12: Use a Kmap to find a minimal expansion as a Boolean sum of Boolean...
 11.4.11.4.13: a) Draw a Kmap for a function in four variables. Put a I in the ce...
 11.4.11.4.14: Use a Kmap to find a minimal expansion as a Boolean sum of Boolean...
 11.4.11.4.15: Find the cells in a Kmap for Boolean functions with five variables...
 11.4.11.4.16: How many cells in a Kmap for Boolean functions with six variables ...
 11.4.11.4.17: a) How many cells does a Kmap in six variables have? b) How many c...
 11.4.11.4.18: Show that cells in a Kmap for Boolean functions in five variables ...
 11.4.11.4.19: Which rows and which columns of a 4 x 16 map for Boolean functions ...
 11.4.11.4.20: Use Kmaps to find a minimal expansion as a Boolean sum of Boolean ...
 11.4.11.4.21: Suppose that there are five members on a committee, but that Smith ...
 11.4.11.4.22: Use the QuineMcCluskey method to simplify the sumofproducts expan...
 11.4.11.4.23: Use the QuineMcCluskey method to simplify the sumofproducts expan...
 11.4.11.4.24: Use the QuineMcCluskey method to simplify the sumofproducts expan...
 11.4.11.4.25: Use the QuineMcCluskey method to simplify the sumofproducts expan...
 11.4.11.4.26: Explain how Kmaps can be used to simplify productofsums expansion...
 11.4.11.4.27: Use the method from Exercise 26 to simplify the productofsums exp...
 11.4.11.4.28: Draw a Kmap for the 16 minterms in four Boolean variables on the s...
 11.4.11.4.29: Build a circuit using OR gates, AND gates, and inverters that produ...
 11.4.11.4.30: In Exercises 3032 find a minimal sumofproducts expansion, given ...
 11.4.11.4.31: In Exercises 3032 find a minimal sumofproducts expansion, given ...
 11.4.11.4.32: In Exercises 3032 find a minimal sumofproducts expansion, given ...
 11.4.11.4.33: Show that products of k literals correspond to 2 nk_ dimensional s...
Solutions for Chapter 11.4: Boolean Algebra
Full solutions for Discrete Mathematics and Its Applications  6th Edition
ISBN: 9780073229720
Solutions for Chapter 11.4: Boolean Algebra
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 11.4: Boolean Algebra includes 33 full stepbystep solutions. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073229720. Since 33 problems in chapter 11.4: Boolean Algebra have been answered, more than 36650 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 6.

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

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

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).

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

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

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).