More doc in the Black Box analisys document

docs/Black_Box_Analysis.md

@@ -19,7 +19,7 @@ This boils down to the fact that, when toggling the clock, the new value of the
 
 ### The Not-So-Black Box
 
-As I hited at in the introduction, a registered PAL device can be viewed as a stateful system, whose current state is dependant on the previous one plus the state of the inputs at the time of moving to the new state.
+As I hinted at in the introduction, a registered PAL device can be viewed as a stateful system, whose current state is dependant on the previous one plus the state of the inputs at the time of moving to the new state.
 
 Luckily for us, the number of the possible states is known and dependant on the number of flip-flops in the device (and, as every flip-flop is connected to a specific output, dependant on the number of so called **registered outputs**). Having said flip-flops directly connected to outputs gives us an important insight on the PAL, as *we know exactly in which state it is at the moment*.
 
@@ -27,3 +27,23 @@ To summarize and simplify, a registered PAL has the following types of outputs:
 
 - **Combinatorial outputs**: their state is dependant on the current state of the inputs and on the current state of the registered output feedbacks.
 - **Registered outputs**: these only change when the clock pin is pulsed, and their new state depends on the state of the inputs and on their own state before the pulsing.
+
+### Exploring the Box
+
+So, we saw that a registered PAL is a state machine, and that the current state is tied to the flip-flops, which are in turn connected to the registered outputs.
+
+The number of these registered outputs is dependant on the PAL model, but fixed and known, and cannot be changed by flashing the device. From this we can gather that **a registered PAL device has 2^X possible states**, where **X is the number of registered outputs for that model**.
+
+We will call these states defined by the registered outputs **MacroStates**, to distinguish them from the **SubStates** which I'll describe below.
+
+While the **MacroState** is defined by the status of the registered outputs, we also need to take into account the state of the normal outputs. As we saw before, an output state is purely combinatorial, and dependant on both the inputs and the registered outputs, and changes without the need of pulsing the clock.
+
+From this we get that for every MacroState we need to test all the input combinations to find the SubStates corresponding to them. For every MacroState we'll have 2^Y, where Y is the number of the combinatorial outputs, possible SubStates, but we'll have to try 2^Z combinations, where Z is the number of the inputs.
+
+#### Some simple math
+
+From what I wrote above, we can see that for a registered PAL we have:
+
+- 2^X theoretically possible MacroStates
+- 2^Z combinations of inputs for every MacroState to map them to the 2^Y possible SubStates for that specific MacroState
+- 2^Z combination of inputs for every MacroState to try with a clock-pulse, to see in which MacroState we end up.