Study of a stack This exercise studies the influence of internal and external faults on failures of a hardware stack. This product, carried out with the aid of a logical circuit, allows to store data by PUSH operations, and to read them in the opposite order of their recording by POP operations.

A typical failure wh ich can affect the stack consists in an overflow, that is to say executing a PUSH when the stack memory is full. To avoid this problem, we add an output signal called Stack_Full which takes' l' when the memory is full and '0' when the stack still has free space. We can nonetheless imagine several faults leading to an overflow despite the presence of this signaling mechanism:

• an internal functional design fault: the size of the stack has been underestimated by the designer,

• an internal hardware fault: a breakdown affects the Stack_Full signal and maintains it at '0' value (no signaling) despite an excessive piling up,

• an external fault: the external circuit uses this stack and ignores the signal Stack_Full.

We should note that a software implementation of this stack could have been carried out using a package which exports the subprograms PUSH and POP and the exception signal Stack_Full. We can imagine similar internal and extern al functional faults as the preceding ones. A fault equivalent to the technological one of non-transmission of the Stack_Full signal will arise if the pro gram language used does not dispose of the exception mechanisms to treat it.

1. For each one of these faults, find a functioning sequence which provokes a stack failure. Does one functioning sequence exists which reveals the presence of one oftwo different faults (producing the same failure)?

2. Imagine several failure situations that would require the use of a Stack_Empty signal.