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Let us define a sequence parity function as a function that takes in a sequence of binary inputs and returns a sequence indicating the number of 1’s in the input so far; specifically, if at time t the 1’s in the input so far is even it returns 1, and 0 if it is odd. For example, given input sequence [0, 1, 0, 1, 1, 0], the parity sequence is [0, 0, 0, 1, 0, 0]. Implement the minimal vanilla recurrent neural network to learn the parity function. Explain your rationale using a state transition diagram and parameters of the network.
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- Simplify the complement of the following function: F(A,B,C,D)=(0,2,4,5,8,9,10,11) Your answer: F=((A'B'D)' (BC)'(AB)')' F=((A'BD)'(BC)'(AB)')' F=((A'B'D)'(B'C)'(AB)') F=((A'B'D')' (BC)'(AB)')Write a program using Scilab that includes the following lines x = linspace(0,1,N); y = sin(%pi*x/2); xi = linspace(0,1,100); The program should use the interp1 function to perform spline interpolation of the (x,y) data at the 100 xi points. These interpolated values should be compared to the exact values of the function sin(π x /2) and your program should use this to find the smallest number of samples N that gives an interpolation with an error of no more than ±0.00001% Define the function f(x) f = @(x) -1*(x < 0) + 1*(x >= 0 & x <= 2); % Set the maximum value of N Nmax = 512; % Initialize the x-axis values for plotting x = linspace(-1,3,1000); % Compute the Fejér sums for various values of N F = zeros(length(x), Nmax); for N = 1:Nmax % Compute the Nth Fejér sum Sn = @(x) 0; for n = 1:N bn = (-1)^(n+1) / (n*pi); Sn = @(x) Sn(x) + bn*sin(n*pi*x); end FN = @(x) (1/N) * Sn(x); % Evaluate the Fejér sum at each point on the x-axis I tried to submit this to MATLAB, but can't seem to get it right.
- Give a transducer TM that takes #bi as input and computes #bi+1, where i is an integer and i>0, and bt is a binary representation of t, for an integer t. For example, if #001 is on the tape as input, then after the TM has executed, the tape should contain #010 in the leftmost cells, with infinite blanks after it. You can assume that the input alphabet is {#,0,1}. If the input is badly formed (e.g., #01# has too many #'s), then the TM can "hang" or go to qr.Consider the code C={00010, 01100,01011,11010,01010}. What is the minimum distance of C? For what k is the code C k-error detecting? Write the set of error patterns that C can detect?The sequence of values: n, c(n), c(c(n)), c(c(c(n))), c(c(c(c(n)))),... is known as the hailstone sequence starting at n. Implement c(n) as a function. Use predicates to test the parity of each input n.
- Make a k-map for each output segment (a, b, c, d, e, f, g) and write a Boolean function which describes each output as a function of inputs (and their complements). Fill in the resulting functions below. a:implement anyEvenBit(x) Return 1 if any even bit in x is set to 1 you are only allowed to use the following eight operators: ! ~ & ^ | + << >> “Max ops” field gives the maximum number of operators you are allowed to use to implement each function /* * anyEvenBit - return 1 if any even-numbered bit in word set to 1* Examples anyEvenBit(0xA) = 0, anyEvenBit(0xE) = 1* Legal ops: ! ~ & ^ | + << >>* Max ops: 12*/int anyEvenBit(int x) {return 2;}Let L={ w in(0 + 1)* 1 | w has even number of 1s}, i.e. L is the set of all bit strings with even number of 1s. Which one of the regular expression below represents L? (A) (0* 10* 1)* (B) 0* (10* 10* )* (C) 0* (10* 1* )* 0* (D) 0* 1(10* 1)* 10*
- Let A = {c, n, b}, B = {x, y} and C = {0, 1}. Find A)A X B X C B)C X B X A C)B X C X CWrite a program that swaps 5th~11th bits in data_a with 25th~31th bits in data_bYour program must work for any data given, not just the example belowIn this question, we assume that the positions of bits count from right to left.That is, the first bit is the least significant bit.data_a DCD 0x77FFD1D1data_b DCD 0x12345678Implement the modular exponentiation (a.k.a. fast exponentiation)function mod_exp (b, n, m) to compute bn (mod m) more efficiently. (Hint: toread n bit-by-bit, use / and % operations repeatedly)a) Test your function for b = 3, n = 231 – 2, m = 231 – 1.b) Report the result and the time (in seconds) it takes to find the result. in pahton