Binary predication from binary variables Logistic Regression generates a binary outcome for a non-binary variable. I need a binary outcome from a binary variable. This is the requirement.


  How to predict binary A using previous values of A?


or


  How to predict binary A,B,C,D values from previous A,B,C,D values?


I know I can gather data and calculate basic probability. I that the most suitable approach? Thank you in advance.
This is really a job for Logistic Regression. Input variables can be categorical/boolean and the prediction can be categorical/boolean as well.

However, if your target variable contains multiple categories, you should use multinomial logistic regression or Ordinal Logistic Regression (if there is an order in your categories). It also changes the way you interpret the output.

The another approach would be to take any nonparametric method, Decision Tree for example. Where input and target can be boolean/categorical/continuous. Note that in case of a categorical variable, it is often recommended to transform it into dummy variables.