(25 p) Problem 2. Consider the following algorithm including 8 steps. S1: START S2: INPUT A, B S3: T = B S4: B = A % B (That means B = A modulo B) S5: A = T %3D S6: IF B>=0_GOTO STEP S3 S7: OUTPUT A S8: END What is the the output of the algorithm for inputs A = 17424 and B = 14568 Output is:
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- PROBLEM 17. [TIME ALLOWED = 5 MINUTES] State whether “n is divisible by 9” is (a) necessary, (b) sufficient, or (c) neither necessary nor sufficient for “n is divisible by 6”, where n is a natural number.Problem #2: [35 pts] Parity Bit CheckerThe parity bit of a sequence of bits is 0 if the number of 1’s in the sequence is even and 1otherwise.Example: if the sequence of bits is 1 1 0 1, the parity bit should be 1 (total number of 1-bits is 3 whichis odd) if the sequence of bits is 1 0 1 0, the parity bit should be 0 (total number of 1-bits is 2 whichis even)Write a Java program that asks the user to enter the number of bits he has. The program thenreads the bits as separate integers. In the end, the program prints the parity bit on the screen. Ifthe use enters a bit value that is neither 0 nor 1, the entry should be discarded and a messagedisplayed as shown in the sample run.Sample run 1:How many bits do you have? 6Enter 6 bits: 1 1 0 0 1 0The parity bit is 1Sample run 2:How many bits do you have? 8Enter 8 bits: 1 1 1 0 0 0 0 1The parity bit is 0Sample run 3:How many bits do you have? 5Enter 5 bits: 1 1 3 0 1Incorrect bit value 3 is discarded.The parity bit is 1 java brogramx^4+2(x^3)-7(x^2)+3=0 a) One of the root of the equation lies in the range (1.0, 2.0). Find this root in 100 iterations using the bisection method. b) Draw the graph of the function between points (0, 2). Your code should include the following steps: • Write the steps of the bisection function (if, else…) and explain each step. (Explain each step in English)• Your code should calculate the root.• Graphic; Variables of x and y axes should be written, x and y axis names should be written, Series should be written to calculate x axis. Use the linspace() for the x series of the graph and section the range 0-2 into 100 pieces. Solve with phyton.
- (Oceanography) The pressure, P, exerted on an underwater object can be determined by this formula: P=gh is the density of water, which is 1.94slug/ft3 . g is the acceleration caused by Earth’s gravity, which is 32.2ft/sec2. h is the object’s depth in the water in feet. a. Determine the units of P by calculating the units resulting from the right side of the formula. Check that your answer corresponds to the units for pressure listed in Table 1.1. b. Determine the pressure on a submarine operating at a depth of 2500 feet.Problem 1 (#2.1.8). Determine whether these statements are true or false. a) ∅ ∈ {∅} b) ∅ ∈ {∅,{∅}} c) {∅} ∈ {∅} d) {∅} ∈ {{∅}} e) {∅} ⊂ {∅,{∅}} f) {{∅}} ⊂ {∅,{∅}} g) {{∅}} ⊂ {{∅},{∅}}x^4+2(x^3)-7(x^2)+3 a) One of the root of the equation lies in the range (1.0, 2.0). Find this root in 100 iterations using the bisection method.b) Draw the graph of the function between points (0, 2).=> Your code should include the following steps:• Write the steps of the bisection function (if, else…) and explain each step. (Explain each step in English)• Your code should calculate the root.• Graphic;Variables of x and y axes should be written,x and y axis names should be written,Series should be written to calculate x axis. Use the linspace() for the x series of the graph and section the range 0-2 into 100 pieces.=>The output of your code should include:• The root of the function• Graph of the function
- 4. Look up the Pythagorean theorem if you are not already familiar with it. Use the following formula to solve for c in the formula: c = √a2 + b2. Use the proper functions from the cmath header file. Be sure to output the result..(Automotive) a. An automobile engine’s performance can be determined by monitoring its rotations per minute (rpm). Determine the conversion factors that can be used to convert rpm to frequency in hertz (Hz), given that 1rotation=1cycle,1minute=60seconds,and1Hz=1cycle/sec. b. Using the conversion factors you determined in Exercise 7a, convert 2000 rpm into hertz.(Thermodynamics) The work, W, performed by a single piston in an engine can be determined by this formula: W=Fd F is the force provided by the piston in Newtons. d is the distance the piston moves in meters. a. Determine the units of W by calculating the units resulting from the right side of the formula. Check that your answer corresponds to the units for work listed in Table 1.1. b. Determine the work performed by a piston that provides a force of 1000 N over a distance of 15 centimeters.
- Q#3 : Write down an algorithm/steps for the following program:PROBLEM 4. [TIME ALLOWED = 5 MINUTES] Give the negation of the following sentence: “It is hot today.”1) a) simplify the following Boolean expression(show all steps): W'X'YZ'+WX'YZ'+WXYZ+W'X'Y'Z'T+W'X'YZ'+WXY'Z+WX'YZ'+WX'Y'Z+W'XYZ+W'X'Y'Z'T' the answer should be X'YZ'+W'X'Z'+WY'Z+XYZ b) prove the equality of these two expressions using a truth table. show all intermediate steps c) show that the simplifcation process in (a) has significantly reduced the number of logic gates required to implement the expression by: * drawing the two networks using only 2-input AND and OR gates. assume that you can use complemented variables as inputs. do not simplify * how many gates have been saved by this simplification ?