Reduce the following state table to minimum number of states using the Implication chart method. Present State Next State Output Inputs (XY) 01 11 10 tz Z 00110000001 10 G G F G G K H G D G G te-Y) e2_c | 1: C F D E | | | | | G | C | | | C | E ax t( x| u e-p N In n- B B H H B F-JE- IBA ABCDEFGHI-JK Solution Step 1: Use X in the square to eliminate output incompatible states. 1stàoutput of A differs from C,D and K so put X in the box B C X D X E F G H I J K X - A B C D E F G H I J àOutput of B differs from C,D,K so put X And repeat the process we get, Output of C differs from E,F,G,H,I,J so put X Output of D differs from E,F,G,H,I,J so put X Output of E differs from K so put X Output of F differs from K so put X Output of G differs from K so put X Output of H differs from K so put X Output of I differs from K so put X Output of J differs from K so put X B C X X D X X E X X F X X G X X H X X I X X J X X K X X X X X X X X - A B C D E F G H I J STEP 2: Here A=B if I=C,C=F A=E if I=C,C=I A=F if B=F,C=I A=G if B=J,I=K,C=G,G=H A=H if B=E,I=F A=I if B=I,C=I,G=D A=J if I=F So table becomes: B I=C,C=F C X X D X X E if I=C,C=I X X F B=F,C=I X X G B=J,I=K, C=G,G=H X X H B=E,I=F X X I if B=I,C=I,G=D X X J I=F X X K X X X X X X X X - A B C D E F G H I J Again similarly for B=E if F=I B=F if B=F,C=I,F=I,G=K B=G if B=J,C=K,F=G,G=H B=H if B=E,C=F,F=C B=I if B=I,C=I,F=I,G=D B=J if C=F,F=C C=K if H=A,D=C,D=E,F=G D=K if H=A SIMILARLY FIND FOR OTHER. SO THE TABLE BECOMES: B I=C,C=F C X X D X X E if I=C,C=I F=I X X F B=F,C=I B=F,C=I, F=I,G=K X X B=F.C=I, G=k G B=J,I=K, C=G,G=H B=J,C=K, F=G,G=H X X B=J,C=K, I=G,G=H F=J,I=K, I=G,K=H H B=E,I=F B=E,C=F, F=C X X B=E,C=F, I=C F=E,I=F, I=C,K=G J=E,K=F, G=C,H=G I if B=I,C=I,G=D B=I,C=I, F=I,G=D X X B=I,C=I G=D F=I,K=D J=I,K=I, G=I,H=D E=I,F=I, C=I, G=D J I=F C=F,F=C X X C=F,I=C F=B,I=F, I=C,K=G J=B,K=F, G=C,H=G E=B I=B, I=F, I=C, D=G K X X H=A,D=C, D=E,F=G H=A X X X X X X - A B C D E F G H I J After this Remove self redundant pairs. X all the squares with implied pairs that are not compatible. Run through the chart until no further X’s are found And then removing all equivalent states. We get final reduced table as below:- Present states 00 01 10 11 output A E F C G 0 B B C I G 0 C H D D F 1 D A C E G 1 F B F C G 0 G E F C G 0 B C X D X E F G H I J K X - A B C D E F G H I J.

1. Reduce the following state table to minimum number of states using the Implication chart
method. Present State Next State Output Inputs (XY) 01 11 10 tz Z 00110000001 10 G G F G G
K H G D G G te-Y) e2_c | 1: C F D E | | | | | G | C | | | C | E ax t( x| u e-p N In n- B B H H B F-JE-
IBA ABCDEFGHI-JK
Solution
Step 1:
Use X in the square to eliminate output incompatible states.
1stàoutput of A differs from C,D and K so put X in the box
B
C
X
D
X
E
F
G
H
I
J
K
X
-
A
B
C
D
E
F
G
H
I
J
àOutput of B differs from C,D,K so put X

2. And repeat the process we get,
Output of C differs from E,F,G,H,I,J so put X
Output of D differs from E,F,G,H,I,J so put X
Output of E differs from K so put X
Output of F differs from K so put X
Output of G differs from K so put X
Output of H differs from K so put X
Output of I differs from K so put X
Output of J differs from K so put X
B
C
X
X
D
X
X
E
X
X
F
X
X
G
X
X
H
X
X
I
X
X
J
X
X
K
X

3. X
X
X
X
X
X
X
-
A
B
C
D
E
F
G
H
I
J
STEP 2:
Here
A=B if I=C,C=F
A=E if I=C,C=I
A=F if B=F,C=I
A=G if B=J,I=K,C=G,G=H
A=H if B=E,I=F
A=I if B=I,C=I,G=D
A=J if I=F
So table becomes:
B
I=C,C=F
C
X
X
D
X
X

4. E
if I=C,C=I
X
X
F
B=F,C=I
X
X
G
B=J,I=K,
C=G,G=H
X
X
H
B=E,I=F
X
X
I
if B=I,C=I,G=D
X
X
J
I=F
X
X
K
X
X
X
X
X
X
X
X
-
A

5. B
C
D
E
F
G
H
I
J
Again similarly for
B=E if F=I
B=F if B=F,C=I,F=I,G=K
B=G if B=J,C=K,F=G,G=H
B=H if B=E,C=F,F=C
B=I if B=I,C=I,F=I,G=D
B=J if C=F,F=C
C=K if H=A,D=C,D=E,F=G
D=K if H=A
SIMILARLY FIND FOR OTHER.
SO THE TABLE BECOMES:
B
I=C,C=F
C
X
X
D
X
X
E
if I=C,C=I
F=I
X
X
F
B=F,C=I
B=F,C=I,

6. F=I,G=K
X
X
B=F.C=I,
G=k
G
B=J,I=K,
C=G,G=H
B=J,C=K,
F=G,G=H
X
X
B=J,C=K,
I=G,G=H
F=J,I=K,
I=G,K=H
H
B=E,I=F
B=E,C=F,
F=C
X
X
B=E,C=F,
I=C
F=E,I=F,
I=C,K=G
J=E,K=F,
G=C,H=G
I
if B=I,C=I,G=D
B=I,C=I,
F=I,G=D
X
X
B=I,C=I
G=D

7. F=I,K=D
J=I,K=I,
G=I,H=D
E=I,F=I, C=I,
G=D
J
I=F
C=F,F=C
X
X
C=F,I=C
F=B,I=F,
I=C,K=G
J=B,K=F,
G=C,H=G
E=B
I=B, I=F,
I=C, D=G
K
X
X
H=A,D=C,
D=E,F=G
H=A
X
X
X
X
X
X
-
A
B
C
D
E

8. F
G
H
I
J
After this
Remove self redundant pairs.
X all the squares with implied pairs that are not compatible.
Run through the chart until no further X’s are found
And then removing all equivalent states.
We get final reduced table as below:-
Present states
00
01
10
11
output
A
E
F
C
G
0
B
B
C
I
G
0
C
H
D
D
F
1
D

9. A
C
E
G
1
F
B
F
C
G
0
G
E
F
C
G
0
B
C
X
D
X
E
F
G
H
I
J
K
X
-
A
B
C
D
E

10. F
G
H
I
J