428 CHAPTER 10 / INTRODUCTION TO SYNCHRONOUS STATE MACHINE DESIGN
with both the a → b and the a → c branching paths. Thus, if
¯
XY → XY while in state
a, malfunction of the FSM is likely to occur. In Fig. 10.9b is the input/state map showing
violation of Eq. (10.4) under input condition XY shared by branching paths a → b and
a → c. Thus, if the mutually exclusive requirement is to hold for a given state, the input/state
map must not have cells containing more than one state identifier.
When Rules Can Be Broken There are conditions under which violation of the sum rule
or of the mutual exclusion requirement is permissible. Simply stated, these conditions are
as follows: If certain branching conditions can never occur or are never permitted to occur,