Summing Series (numeric summation): Tylor Series: x2 x3 x 5! " -1-x+ 2 3! e-X = ....... 4! n=0 Calculate the exact exponent for x-0.1 and the summing series upto the Oterm that reaches the machine percision? Error Nth term/sum <10^(-16)
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- C++ Program: Make a program that would demonstrate the concept of Line Coding: Polar NRZ: Remember: if next bit is 1, there is inversion if next bit is 0, no inversion neg – means the signal is in the negative axis pos – means the signal is in the positive axis inv – means there is inversion no inv – means there is no inversion a. initially high (starts with positive, inverse is negative) Input: 1 1 1 0 0 1 0 1 1 0 0 0 Output: inv neg inv pos inv neg no inv neg no inv neg inv pos no inv pos inv neg inv pos no inv pos no inv pos no inv pos b. initially low (starts with negative, inverse is positive) Input: 1 1 1 0 0 1 0 1 1 0 0 0 Output: inv pos inv neg inv pos no inv pos no inv pos inv neg no inv neg inv pos inv neg no inv neg no inv neg no inv neg The logic here is when input is 1, next inputted 1 will be inverse…Using the laws of boolean algebra simplify these expressions and LIST the laws used to justify each step. . Each final result should be expressed as a sum of products of literals, where each product uses the smallest number of literals. a. ABC + ABC’ + A’C + A’B’C + AB’C b. A'B' + A'BC' + (A + C')' c. A' + A'B'CD' + A'B'C'D' + AB'C' + AB'CD' + ABD + BC'DOpenMP C++ With the following code, create 3 versions: Outer loop parallelism: use a single OpenMP pragma only at the outer loop Inner loop parallelism: use a single OpenMP pragma only at the inner loop (use reduction) Nested loop parallelism: use pragmas at both the outer loop and inner loop ----- #pragma omp parallel for for(int i = 0; i < n; i++) { #pragma omp parallel for for(int j = 0; j < n; j++) { y[i] += A[i * n + j] * x[j]; } }
- Coding in Python with NumPY and Matplotlib functions. Suppose x has values of 0.0, 1.5, 2.4, 4.2 and y has values 12.5, -3.0, 6.4, 32.1 Plot the x, y pairs on a graph as square markers of magenta color. Do not draw a curve through the data points.EXAMPLE: Kocher’s timing attacks on cryptosystems illustrate this [1084]. Kocher notes that the instructions executed by implementations of cryptosystems depend on the setting of bits in the key. For example, the algorithm in Figure 9–7 implements a fast modular exponentiation function. If a bit is 1, two multiplications occur; otherwise, one multiplication occurs. The extra multiplication takes extra time. Kocher determines bits of the confidential exponent by measuring computation time x:= 1; atmp := a; for 1 := 0 to k-1 do begin If Zi = 1 then x := (x * atmp) mod n; atmp := )atmp * atmp) mod n; end; result := x; Figure 9–7 A fast modular exponentiation routine. This routine computes x = az mod n. The bits of z are zk–1... z0. Kocher’s attack derives information about the computation from the characteristic of time. As a cryptographic key is confidential, this is a side channel attack. This is an example of a passive side channel attack, because results are derived only from…Elimination of an arbitrary constant by erasure is a valid mathematical operation. True or False
- Write the symbol used in the following language of mathematics: 1. The complement of the complement of A 2. The set of rational numbers 3. The Cartesian product of B and C 4. 3 is an integer 5. The value of y ranges from -4 to 5 6. The square of a number is positive 7. J belongs to both sets A and B 8. Point A's distance from D is equal to point B's distance from DThe generating function for the sequence 1,0,1,0,1,0,1 is____ a)1 + x + x2 + x3+ x4+ x5 + x6+…. b)1 +x2 + x4+ x6+……. c)1 + x+ x2 + x3+ x4+ x5 + x6 d)1 + x2 + x4+ x6Determine the complexity and count the primitive operation. Show your solution on counting and adding the sum of primitives public static void main(String[] args) {Scanner scanner = new Scanner(System.in);System.out.print("Enter a number for count:");int n = scanner.nextInt();for(int i = 1; i <= n; i++){System.out.print(printFibonacci(i) + " ");}input.close();private static int printFibonacci(int cNumber){if(cNumber == 1 || cNumber == 2){return 1;}return printFibonacci(cNumber - 1) + printFibonacci(cNumber - 2);}}
- 3. using python code The function y(x) represented by the data below has maximum at x =0.7692. Compute ths maximum by Neville's interpolation overfour nearest- neighbor data points. x = 0 0.5 1 1.5 2 2.5 3 y=1.8421 2.4694 2.4921 1.9047 0.8509 -0.4112 -1.5727A Sequence Detector is a circuit which given an input string of bits generates an output 1 whenever the target sequence (pattern) has been detected. There are two types of sequence detectors: Overlapping: The detector allows overlapping, hence the final bits of one sequence can be the start of another sequence. Non-overlapping: The detector does not allow overlapping, hence a new sequence starts only after the previous sequence is completed. Ex: Detect pattern 101 For non-overlapping case: Input :0110101011001 Output:0000100010000 For overlapping case: Input :0110101011001 Output:0000101010000 Design a sequential circuit (overlapping) with an input ‘x’. The pattern to be detected is the binary number that is equal to 1001100 For example,the circuit detects the sequence 00010 . When the sequence is detected, the detector outputs z=‘1’ For this circuit: Draw the ASM diagram. Construct the state table. Draw the logic circuit for the datapath and control in logisim.Input: (1) A real number x0, (2) n integer coefficients {a0, a1, …, an-1} Output: P(x0)=a0+a1x0+a2x02+…+an-1x0n-1 (a) Give or cite an efficient EREW PRAM algorithm (idea) to output P(x0). (b) What is the total time needed in your algorithm? Please explain the time needed for each part.