a) f(x) = x{x-2) (x-)(x+1} b) f(x) =-(x-2) {x-1)(x+1) ) f(x) =-x{x-1){x+)(x- 2}' a) f(x) -(1-x)(x+1)° (x- 2) Write c++ code that will output all the values of f(x) given values of x. Do it for a, b, c and d above.
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- Simplify the following Boolean expressions, using four-variable maps: (a) A'B'C'D' + AC'D' + B'CD' + A'BCD + BC'D (b) x'z + w'xy' + w(x'y + xy') (c) A'B'C'D + AB'D + A'BC' + ABCD + AB'CMatlab Write a program to plot the relation of the following functions y1=sin(x),y2=sin(4x),y3=cos(6x),y4=sin(5x)cos(3x) ,that shows these graphs with interval [0,4π],and increasing π /50 for each step .Simplify the following Boolean expressions, using four-variable K-maps: AB′C+B′C′D′+BCD+ACD′+A′B′C+A′BC′D
- Prove by Systematic Semantic Tableaux ∃xR(x,x)∨∃x[R(x,x)→¬∃yR(y,x)]4. Simplify the following Boolean expressions, using four-variable K-maps: (a) A′B′C′D′+AC′D′+B′CD′+A′BCD+BC′D (b) w′z+xz+x′y+wx′zSimplify Boolean function using K map. Variables are marked in a,b,c,d order 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 Question 37 options: ac’ + ad + bd + a’c ac’ + bd’ + a’c ac’ + bd + a’c None of above c’a + b’c’ + ab
- Simplify the following Boolean function , using three- variable maps: a) F(x,y,z) = Σ (0,2,6,7) b) F(A,B,C ) = Σ (0,2,3,4,6) c) F(a,b,c) = Σ (0,1,2,3,7) d) F(x,y,z) = Σ (3,5,6,7)Suppose N is an RSA modulus, and x^2 ≡N y^2, but x≡N ±y. Show how to efficiently factorN when such a pair x and y are known. ************* WRITTEN AS A SAGE FUNTION*****************Consider a language with only three letters, x, y, and z. Now suppose that you intercept a very long message in this language and discover the average frequencies for x, y, and z to be 0.6, 0.3, and 0.1, respectively. Based on your observations, what is the index of coincidence for this language
- Consider the degree-4 LFSR given by x to the power of 4 space plus space x squared space plus space x space plus space 1. Assume that the LFSR is initialized with the string left parenthesis s subscript 0 s subscript 1 s subscript 2 s subscript 3 right parenthesis equals left parenthesis 0110 right parenthesis. How long is the cycle generated?Simplify the following expression using K-Maps F(A,B,C,D)=A′C′+A′B′+ACD′+BC′DPlease explain all steps: What Boolean equation is represented by the following K-Maps: a) ~y~z ~yz yz y~z ~x 1 1 1 x 1 1 1 1 b) ~y~z ~yz yz y~z ~w~x 1 1 ~wx 1 1 wx 1 w~x 1 1 c) ~y~z ~yz yz y~z ~w~x 1 1 1 1 ~wx 1 1 wx 1 1 1 1 w~x 1 1 d) ~y~z ~yz yz y~z ~w~x 1 1 ~wx 1 1 1 wx 1 1 w~x 1 1 1