4. (Coding) Implement the Perceptron algorithm and run it on the following synthetic data sets in R10: pick w* = [1,0,0, ,0]; generate 1000 points x by sampling uniformly at random over the unit sphere and then removing those that have margin y smaller than 0.1; generate label y = sign((w*)"x).

Implement 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

Bottom: Given b, set the low-order b bits of x to 1; the others to 0. For example, if b is 3, x should be 7. Pay special attention to the edge cases: if b is 32 x should be −1; if b is 0 x should be 0. Do not use - in your solution. Write code in Java. Provided input(s): b Permitted: 40 operations (may use !, ~, +, <<, >>, &, ^, |) Hint: The obvious solution ~(0xFFFFFFFF << b) won’t work. Bit shifts always do a modulo on their right-hand operand, so a << b does the same thing as a << (b % (8*sizeof(a)). Thus, << 32 and << 0 do the same thing.