Creating hypothesis Adaboost

I have been struggling for a couple of days with this, without being able to find a clear answer. I am learning Adaboost algorithm, but how the different hypothesis are created stays very unclear for me. I have read about Decision stumps as a base learner, but I am interested in Bayesian approach. Let's say I have this simple data set: enter link description here -- link to google drive with the sample data set ( I am new user and cannot post images) where D1 is the expected output. I have read how to reweight and calculate the error, but how do we create the hypothesis h(x) in the first place I could not understand.

I have started calculating the weights directly, so for the first row each data point has equal 1/8 weight and 3 data points make an error. So the error rate should be 1/8+1/8+1/8. Then I calculate the new weights - 1/2*(W(s)/1-E) for the right classified entries and 1/2*(W(s)/E) -for the wrong ones, where E is the error rate . But this just seems not to be the correct way.(on the second picture there is the only example with value calculation in every step) Thanks in advance