1. COE 202: Fundamentals of Computer Eng. (T061) Dr. Marwan Abu-Amara Equivalent States

2. COE 202 (T061) – Dr. Marwan Abu-Amara 2 Definition 2 states are equivalent if for each possible input:  Both states give exactly same output and go to same next state, or  Both states give exactly same output and go to same equivalent next states

3. COE 202 (T061) – Dr. Marwan Abu-Amara 3 Example PresentNext StateOutput Statex = 0x = 1x = 0x = 1 acb01 bda01 cad10 dbd10 States a & b have same output for the same input Next states for a & b:  c & d for x = 0  b & a for x = 1 If c & d are equivalent, then a & b are equivalent because same or equivalent next states  (a, b) imply (c, d) States c & d have same output for the same input Next states for c & d:  a & b for x = 0  d & d for x = 1 If a & b are equivalent, then c & d are equivalent because same or equivalent next states  (c, d) imply (a, b)

4. COE 202 (T061) – Dr. Marwan Abu-Amara 4 Example … PresentNext StateOutput Statex = 0x = 1x = 0x = 1 aca01 cac10 Since (a, b) imply (c, d) and (c, d) imply (a, b), then both pairs are equivalent  a equivalent to b  c equivalent to d

5. COE 202 (T061) – Dr. Marwan Abu-Amara 5 Implication Table Chart that consists of squares, one for every possible pair of states, that provide spaces for listing any possible implied states  Triangular table with (n – 1) rows & (n – 1) columns, where n = # states  Columns:states 1  (n – 1)  Rows:states 2  n  Place “x” if 2 states are NOT equivalent  Place “ ” if 2 states are equivalent  Place “condition” for 2 states to be equivalent  Go over all table entries until they are marked as either “x” or “ ”

6. COE 202 (T061) – Dr. Marwan Abu-Amara 6 Example PresentNext StateOutput Statex = 0x = 1x = 0x = 1 adb00 bea00 cgf01 dad10 ead10 fcb00 gae10 b c d e f g abcdef d, e x x x c, d x x x x c, e a, b x x x x x x d, e x x x x  (a = b) and (d = e = g)

7. COE 202 (T061) – Dr. Marwan Abu-Amara 7 Example … PresentNext StateOutput Statex = 0x = 1x = 0x = 1 ada00 cdf01 dad10 fca00