Show that x^5y^3+x^4y^4+x^3y^5 is Ω(x^3y^3).
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Show that x^5y^3+x^4y^4+x^3y^5 is Ω(x^3y^3).
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Solved in 3 steps with 1 images
- Show that (x^3+2x)/(2x+1) is O(x^2).procedure Horner(c, a_(0), a_(1), a_(2),… , a_(n): real numbers)y := a_(n)for i := 1 to ny := y ∗ c + a_(n−i)return y {y = a_(n)c^(n) + a_(n−1)c^(n−1) + ⋯ + a_(1)c + a_(0)}a) Evaluate 3x^(2) + x + 1 at x = 2 by working througheach step of the algorithm showing the values assigned at each assignment step.b) Exactly how many multiplications and additions areused by this algorithm to evaluate a polynomial ofdegree n at x = c? (Do not count additions used toincrement the loop variable.)iii. 5+ 2cos(n) = Theta (1) iv. Show that (3/2)n^2 +2n-3 = Q (n^2)
- Function minimization using Karnaugh-Maps. 1. 2. AB 10 11 lo 0 Bc 00 0 00 01 1 lo - 11 0 F (A, B, C, D) O 9 D lo 1 9 P 10 1 0 0 01 11 1 D 9 T - 0 7 O A = 0 E F (A, B, C, D, E) = D 0 Û Bc DE 00 01 11 of 0 00 01 11 01 0 O O 0 21 O 0 to 0 0 TE 1 9we represent the finite-length signals as vectors in Euclidean space, many operations on signals can be encoded as a matrix-vector multiplication. Consider for example a circular shift in C: a delay by one (i.e. a right shift) transforms the signal x = (xo X1 X2]" into x = [xı xo xz]" and it can be described by the matrix TO D = [0 1 0'0 0 1'1 0 0] so that x = Dx. Determine the matrix F that implements the one step difference operator in C ie the operator that transforms a signal x into [(x - x)(x1 - x0)(x2 - 1)]Q2) Consider a (7,4) code with generator matrix G=[ 1 1 0 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 1 0 0 0 1 ] , Encode the messages 1110, 1010, 0001.
- Consider the following multiplication problem: where each P stands for a (possibly different) prime digit (so 2, 3, 5 or 7).Formulate this problem as a CSP. For your information: this problem has a unique solution, namely: see image below:Let C be the binary linear code with basis B = (0011001, 1000010, 1111111) with information bits in positions 2, 4, and 6. State the codeword x that encodes the message m = 110: Tip You can solve equations and use row reductions here- but since the basis is smal, it might be easiest just to look at its codewords and use intelligent trial and error. A correct answer is 0111101, which can be typed in as follows: 0111101 Let Cbe the cnde cansiseliminate arbitrary constant: a. y^2 = 4ax b. y = cx + c^2 + 1 c. y = A + Bx + Cx^2 - 2x^3