Question 1: A Multiplexer (MUX)

a) Write truth table and draw symbol for a 4-to-1 MUX. (1 mark)

b) Write VHDL code for the above multiplexer. (1 mark)

c) Write VHDL code for a test bench and simulate the design. (1 mark)

d) Implement the design on FPGA, with inputs connected to switches and output to LED. (1 mark)

4. On January 1, Year 1, Taxpayer (“T”) purchased both a bond and stock of Corporation X. The bond was purchased for $10,000, had a face value of $10,000 and paid 10% interest ($1,000) on December 31 of each year. The stock was purchased for $10,000 and paid a dividend of $1,000 on December 31, ex- dividend date December 15. T sold both the X stock and the X bond on July 1, of Year 1. The bond sold for $10,300 and the stock sold for $11,000. What income, gain or loss, including character type (e.g. capital gain, interest, dividend, ordinary) will T recognize as a result of the sales? __________________________________ BOND __________________________________ STOCK

1. Assume we have the following resources: • 4 graphic displays • 3 printers • 1 disks Consider we have already allocated these resources among four processes as demonstrated by the following matrix named Allocation. Process Name Graphics Printers Disk Drives Process A 0 1 0 Process B 0 0 1 Process C 0 1 0 Process D 1 0 0 The following is the matrix to show the number of each resources requested; we call this matrix Request. Process Name Graphics Printers Disk Drives Process A 2 0 0 Process B 2 2 0 Process C 1 0 1 Process D 0 2 1 a. Apply Deadlock Detection Algorithm and check whether any deadlock exists. b. Suppose now the Process B requests one additional instance of Graphics, and Process C requests two additional instances of Graphics and one additional instance of Disk Drives, whether this can be granted?

use for and while loop, also ifstream, ofstream, setprecision, and iomanip.

Pi = 4 * (1/1 – 1/3 + 1/5 – 1/7 + 1/9 … (alternating + -) (1/n))

First, Pi should be a double to allow many decimals. Notice that the numerator is always 1 or -1. If you started the numerator at -1, then multiply each term by -1. So if started the numerator at -1 and multiplied it by -1, the first numerator will be 1, then the next the numerator will be -1, alternating + and -.

Then notice that the denominator goes from 1,3,5,7,9 etc. So this is counting by 2s starting at one. For loops are good when you know how many times it will go through the loop. So a for loop might be something like:

for (long denom=1; denom <n; denom=denom+2)
where denom(inator) is the term that changes by 2 starting at 1 (not zero). We use a long to allow very large numbers

• Remember, not every for loop starts at one, and not every for loop ends in i++!
• Also remember that an int divided by int (or long/long) is an int, so you will have to convert the right hand side like double( 1/1 – 1/3 + 1/5)
• Note that 4 is multiplied outside the loop (after we have our series determined)

We are using longs, so we can have very long numbers. Likewise, PI should be a double (not a float) to have a very large decimal accuracy

Write a c++ program to calculate the approximate value of pi using this series. The program takes an input denom that determines the number of values we are going to use in this series. Then output the approximation of the value of pi. The more values in the series, the more accurate the data. Note 5 terms isn’t nearly enough to give you an accurate estimation of PI. You will try it with numbers read in from a file. to see the accuracy increase. Use a while loop to read in number of values from a file. Then inside that loop, use a for loop for the calculation

• Create an input file called lab04in.txt. Place the following numbers in the file. Read in long data types (instead of int)

12

123

1234

12345

123456

1234567

12345678

123456789

For this problem, use an annual interest rate of 4%.

On 1/1/2020, you buy a perpetuity paying you $10,000 at the beginning of each year, commencing on 1/1/2020.  (Recall that a perpetuity is an annuity that does not end.)

(a)        Calculate the present value of the perpetuity as of 1/1/2020.

(b)       After receiving exactly ten payments, you exchange the perpetuity on 1/1/2030 for an annuity paying $x at the beginning of each year for 20 years, commencing on 1/1/2030.  (Note:  Since you have received exactly ten payments, you exchange your perpetuity on 1/1/2030 before receiving the payment of $10,000 on that day.)

What is the present value of your perpetuity on 1/1/2030 when you exchange it?

(c)        Without any calculations, conclude whether $x is greater than, equal to, or less than $10,000.  Explain.

(Note:  A correct answer without a correct explanation earns no credit.)

(d)       Calculate $x.

4. On January 1 of Year 1, Congo Express Airways issued $4,600,000 of 7%, bonds that pay interest semiannually on January 1 and July 1. The bond issue price is $4,280,000 and the market rate of interest for similar bonds is 9%. The bond premium or discount is being amortized using the straight-line method at a rate of $10,000 every 6 months. The life of these bonds is:

9. Caitlin, Chris, and Molly are partners and share income and losses in a 3:4:3 ratio. The partnership’s capital balances are Caitlin, $132,000; Chris, $92,000; and Molly, $112,000. Paul is admitted to the partnership on July 1 with a 20% equity and invests $172,000. The balance in Caitlin’s capital account immediately after Paul’s admission is:

14. Caitlin, Chris, and Molly are partners and share income and losses in a 3:4:3 ratio. The partnership’s capital balances are Caitlin, $132,000; Chris, $92,000; and Molly, $112,000. Paul is admitted to the partnership on July 1 with a 20% equity and invests $172,000. The balance in Caitlin’s capital account immediately after Paul’s admission is:

16. Barber and Atkins are partners in an accounting firm and share net income and loss equally. Barber's beginning partnership capital balance for the current year is $286,000, and Atkins' beginning partnership capital balance for the current year is $167,000. The partnership had net income of $172,000 for the year. Barber withdrew $57,000 during the year and Atkins withdrew $45,000. What is Atkins's return on equity?

. Use the Taylor expansion of the function f(z) = 1 1+z [8] 4 centred at the origin z = 0, together with the extended Cauchy Integral Formula to evaluate the contour integrals I C dz/ z^ k (z^ 4 + 1), k = 0, 1, . . . , where C is any positively oriented simple contour going around the origin that is interior to the circle of radius 1 centred at z = 0.

1. Use induction to prove that Summation with n terms where i=1 and Summation 3i 2 − 3i + 1 = n^3 for all n ≥ 1.

2. Let X be the set of all natural numbers x with the property that x = 4a + 13b for some natural numbers a and b. For example, 30 ∈ X since 30 = 4(1) + 13(2), but 5 ∈/ X since there’s no way to add 4’s and 13’s together to reach 5. (It’s not a multiple of 4, and adding 13 goes over.) Use strong induction to prove that n ∈ X for all integers n ≥ 36. Hint: it should be easy to show that k + 1 ∈ X if k − 3 ∈ X. You may need multiple base cases for this problem

Sentinel Company is considering an investment in technology to improve its operations. The investment will require an initial outlay of $259,000 and will yield the following expected cash flows. Management requires investments to have a payback period of 3 years, and it requires a 9% return on investments. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the table provided.)

Required:
1. Determine the payback period for this investment.
2. Determine the break-even time for this investment.
3. Determine the net present value for this investment.

1.

2.

3.