Notions and theorems of elementary formal logic by Witold Pogorzelski

By Witold Pogorzelski

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S2 - 110 l1 {s1,s3}101 l0 {s0,s1}111 Dd2Dd1Dd0 st. s1,s2 {s1} d1,101,111 s2,s4 {s1,s4} d2,111 s2 h =1 ‘1’ on common position 0 0 0 4 -1 3 2 1 1 -1 3 3 3 s0 s3 s3 {s0,s3} 111 s1 s4 s2 s1,s2 {s1} d1,101,111 sum Fig. 15 The example IDT: last step of state assignment -0 11 01 011 10 100 01 011 st0 st0 st0 st1 st1 st1 st2 st2 st2 st3 st3 st0 st0 st1 st1 st0 st2 st2 st1 st3 st3 st2 0 0 1 0 1 1 1 1 1 1 State assignment s0 s1 s2 s3 - 0001 0010 0100 1000 Fig. 16 State transition table of the lion FSM [14] with example state codes Let’s implement the output function by means of a 3-term PAL-based cells.

If there exists state Si such that η Si > k and as an effect of two-level minimization the number of implicants corresponding to transition to state Si will not be reduced to k or less, the structure will be multi-cell level. 5). The number of logic levels of fast automata must be as few as possible. Moreover the number of logic levels must be controlled during the state assignment, especially for transition block. It is necessary to appraise the number of logic levels of the transition block before state assignment.

3 Primary Merging Conditions 29 input X and the same next state Si , binary codes that differ only in one position, ν (S p , Sr ) = 1. Two implicants are covered by means of one implicant as an effect of two-level minimization. 4 A fragment of an example FSM with state assignment is shown in Fig. 4. There are two transitions presented in the figure. The state s3 is the next state for both transitions. The inputs and the outputs are also the same for both transitions. The present states are s1 in first transition and s2 in the second transition.

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