Multiplication can be thought of as repeated addition. Three times four is 4 added to itself 3 times.

1) Create an assembly program that multiplies two 8 bit integers (2's complement) together in your PIC, using the repeated summation technique.

2) Add a feature to your program that detects if the answer is too big to hold in 8 bit 2's complement notation

3) The repeated summation algorithm is slow. In a previous homework we developed a technique for multiplying that used bit shifting, that significantly reduces the number of loop iterations needed. Write a PIC assembly program to multiply two 8 bit integers (2's complement) together using this technique. [Hint: be careful of the carry bit.]

4) Develop a PIC routine to perform integer division of two positive 8 bit (2's complement) numbers, using a repeated subtraction algorithm. Report both the quotient and the remainder.

5) Develop a PIC routine to perform integer division of two positive 8 bit (2's complement) numbers, using long division (adapted for binary numbers). Report both the quotient and the remainder.

When a fair die is rolled n times, the probability of getting at most two sixes is 0.532 correct to three significant figures. (a) Find the value of n. ( Can help without using a GDC or write down steps on how to find answer from GDC. not just stating .. I know the answer is 15 but l need working steps on how to get 15 clear?)

A maximal plane graph is a plane graph G = (V, E) with n ≥ 3 vertices such that if we join any two non-adjacent vertices in G, we obtain a non-plane graph.

a) Draw a maximal plane graphs on six vertices.

b) Show that a maximal plane graph on n points has 3n − 6 edges and 2n − 4 faces.

c) A triangulation of an n-gon is a plane graph whose infinite face boundary is a convex n-gon and all of whose other faces are triangles. How many edges does a triangulation of an n-gon have?

100 students were asked to ll out a form with three survey questions, as follows: H: Honor Roll
C: Club membership (Robotics Club or Gaming Club)
D: Double-major

Survey results were as follows:

28 checked H (possibly non-exclusively), 26 checked C (possibly non-exclusively), 14 checked D (possibly non-exclusively)

8 checked H and C (possibly. non-exclusively), 4 checked H and D (possibly. non- exclusively), 3 checked C and D (possibly. non-exclusively)

And 2 checked all three statements.
1. How many students didn't check any of the boxes?

2. How many students checked exactly two boxes?
3. How many students checked at LEAST two boxes?

4. How many students checked the Clubs box only? [d]

Determine whether the lines ?1:?=6+3?,?=6+2?,?=13+4? and ?2:?=−11+4??=−8+4??=−13+7? intersect, are skew, or are parallel. If they intersect, determine the point of intersection; if not leave the remaining answer blanks empty.

(Lower bound for searching algorithms) Prove: any comparison-based searching algorithm on a set of n elements takes time Ω(log n) in the worst case. (Hint: you may want to read Section 8.1 of the textbook for related terminologies and techniques.)

Determine whether S = { (1,0,0) , (1,1,0) , (1,1,1) } Is a basis for R^3 and write (8,3,8) as a linear combination of vector in S.

Please explain in details how to solve this problem.

Write a Matlab program to create specialized plot animation with 16 frames by using fast
Fourier transforms of complex matrices

Find the general solution of the differential equation using the method of undetermined coefficients y" + y' - 6y = x^2

Write your own routine to solve a system of n linear equations and n unknowns using the LU decomposition. Input should take an augmented matrix and the number of equations n. Output should be the augmented matrix. L and U matrices and the solution. Also compare your results to those of Matlab’s built in LU decomposition. Use your code to solve the systems given as (a) and (b) below: a) 3a − 2b + c = −3, a − 4b + 2c + 2d = 6, a + 3b = 5, −3a + 7b + 9c + d = 5

Using matlab

Find x and y that solve the following system: ln(x 2 + y) = 1 − y , xy = − √ x

Runaways The FBI has stated that most runaways are females. A recent sampling of 90 cases involving runaways indicated that 63 of them were female.

a. What is the inherent question of interest here?

b.What might be a reasonable description of the population of interest?

c.What is the relevant sample here?

d.What is the random variable being evaluated here?

e.What is the population parameter of interest?

f.What is this parameter’s corresponding sample statistic?

g.What is an appropriate research hypothesis to consider?

h.What is the corresponding null hypothesis?

i.What is the test statistic used to test these hypotheses?

j.What is the null distribution of this test statistic?

k.What is the decision rule that might be used here?

l.What decision was made with regard to the null hypothesis?

m.What is your conclusion based on the available data?