This preview shows page 1. Sign up to view the full content.
Unformatted text preview: ows:
1. Construct chart containing a square for each pair of states.
2. Compare each pair of rows in the state table:
If the outputs associated with states i and j are different, place an X in
square ij to indicate that i /≡ j.
If the outputs are the same, place the implied pairs in square ij.
(If the next states of i and j are m and n for some input x, then mn is an
implied pair.)
If the outputs and next states are the same (or if ij only implies itself), place
a check (√) in square ij to indicate that i ≡ j. 3. Go through the table squarebysquare. If square ij contains the implied
pair mn, and square mn contains an X, then i /≡ j, and an X should be
placed in square ij.
4. If any X’s were added in step 3, repeat step 3 until no more X’s are
added.
5. For each square ij which does not contain an X, i ≡ j. Section 15.3 (p. 481) Equivalent Sequential Circuits
Definition 15.2:
Sequential circuit N1 is equivalent to sequential circuit N2 if
for each state p in N1, there is a state q in N2 such that p ≡ q,
and conversely, for each state s in N2, there is a state t in N1
such that s ≡ t. Section 15.4 (p. 481)
Figure 156: Graphs for Equivalent Circuits Incompletely Specified State Tables
Assume that A can only generate two possible output
sequences, X = 100 and X = 110. Thus B has only two possible
input sequences. Also, C only reads Z during everything third
input. Figure 158 Figure 157: Implication Tables for Determining Circuit Equivalence
Table 155. Incompletely Specified State Table Derivation of FlipFlop Input Equations
After state minimization, use the following procedure to get flipflop
input equations: 1. Assign flipflop state values to correspond to the states in the
reduced table.
2. Construct transition table for next states of the flipflops as
function of the present states and inputs.
3. Derive the nextstate maps from the transition table.
4. Find flipflop input maps from the nextstate maps using the
techniques developed in Unit 12 and find the flipflop input
eq...
View
Full
Document
 Spring '08
 Brown

Click to edit the document details