Consider the sequence g0 = 1,
g1 = 1, g2 = 21,
g3 = 41, g4...
Consider the sequence g0 = 1,
g1 = 1, g2 = 21,
g3 = 41, g4 = 461,
g5 = 1281, g6 = 10501,...
whose linear generator is gn+2 =
gn+1 + 20gn, that is, 20(!)
pairs of baby rabbit offspring.
As we did for the Fibonacci numbers, please derive a closed
form expression for gn.
Consider the sequence hn =
(–1)n gn:
1,–1,21,–41,461,–1281,10501,... Please give a second order
homogeneous linear recurrence with constant coefficients for
hn and prove that...
(a)
For the following quadratic forms gi(x) write down the
associated symmetric matrix Ai such that...
(a)
For the following quadratic forms gi(x) write down the
associated symmetric matrix Ai such that gi(x) = xT Aix.
g1(x1, x2) = x21 − 2x1x2 + 4x2
g2(x1, x2) = 4x21 − 6x1x2 + x2
g3(x1, x2, x3) = 3x21 + 3x2 + 5x23 + 2x1x2 − 2x1x3 − 2x2x3
g4(x1, x2, x3) = −3x21 − x2 + 8x2x3 − 16x23
(b) Determine the definiteness of g1(x) and g3(x) using the
method of eigenvalues.
(c) Determine the definiteness of...
f(a,b,c) =
Xm(0,1,5)
Use boolean algebra to simplify both of the above expressions to
determine the...
f(a,b,c) =
Xm(0,1,5)
Use boolean algebra to simplify both of the above expressions to
determine the minimal sum-of-products and the minimal
product-of-sums representation for the above function.
Logic Circuit
Problem #3
Given the following logic function: F(a,b,c,d) = ?
m(0,3,7,9,11,13,15)+?d(4,6,8) use a Karnaugh...
Logic Circuit
Problem #3
Given the following logic function: F(a,b,c,d) = ?
m(0,3,7,9,11,13,15)+?d(4,6,8) use a Karnaugh Map to, a) Find a
minimal SOP expression Answer: F(a,b,c,d) = b) Find a minimal POS
expression
Answer: F(a,b,c,d) =
Problem #4
Implement the function F(a,b,c,d) given in problem #3 using two
3-to-8 decoders, both active low enabled and active low output.
F(a,b,c,d) = ? m(0,3,7,9,11,13,15)+?d(4,6,8)
Answer:
Problem #5
Implement the function in the previous problem: F(a,b,c,d) = ?
m(0,3,7,9,11,13,15)+?d(4,6,8), using a single 4...
Let A = (−5,3,5), B = (−10,0,2), C = (−5,0,−3), and D =
(0,3,0).
a) Find...
Let A = (−5,3,5), B = (−10,0,2), C = (−5,0,−3), and D =
(0,3,0).
a) Find the area of the parallelogram determined by these four
points.
b) The area of the triangle ABC
c) The area of the triangle ABD.