Hardware Reference
In-Depth Information
Figure 3.14
Safe-machine analysis. (a) Example with three states and sequential encoding. (b) Corresponding
truth table for
nx_state
. (c) Resulting Karnaugh maps. (d-f) Three compositions for the critical
(free-i lling) columns. (g) Resulting system if the option in f is used. (h) Optimal expressions for
nx_state
, which coincide with the (bad) case of e.
Note that the use of an explicit reset signal only prevents the i rst possibility, not
the effect of noise. Consequently, for a truly safe FSM, the external states must also
be considered when the expressions for
nx_state
are developed. Other, less usual
mechanisms also exist, including the use of a watchdog that resets the machine in
case it remains in the same state longer than a predei ned time limit, but this
would obviously be applicable only if the machine were expected to change its
state periodically.
A detailed example is presented in i gure 3.14. The actual machine states are A1-A3.
Because sequential encoding is used (note the codewords below the state circles in
i gure 3.14a), two bits are needed, resulting in one external state (B). We want to
examine the conditions needed for this machine to be able to recover in case state B
happens.
By the method of section 3.3, the truth table for
nx_state
shown in i gure 3.14b is
obtained, from which the Karnaugh maps of i gure 3.14c result. Note in the latter that
