b
ci
cf
c
d
cd, de,
fg
e
ci
fi
f
bf, ci,
gk
bf, ci,
fi, gk
bf, ci
gk
g
bj, cg,
ki, gh
bj, ck,
fg, gh
bj, ck,
gi, gh
fi, ik,
gi, hk
h
be, fi
be, cf
be, cf,
ci
ef, fi,
ci, gk
ej, fk,
gh, cg
i
bi, ci,
dg
bi, ci,
fi, dg
bi, ci,
dg
dk
ij, ik,
gi, dh
ei, fi,
ci, dg
j
fi
cf
cf, ci
bf, fi,
ci, gk
bj, fk,
cg, gh
be
bi, ci,
dg, fi
k
ah, de,
cd, fg
ah
a
b
c
d
e
f
g
h
i
j
From the implication table, we have found that a
≡
h
≡
j, b
≡
e, d
≡
k, and f
≡
i.
The equivalence classes are {a, h, j},
{b, e}, {c}, {d, k}, {f, i}, and {g}.
To represent the minimized state table, we must have one state from each of the
equivalence classes.
PS
x
1
x
2
z
00
01
11
10
a
b
f
c
g
0
b
b
c
f
g
0
c
a
d
d
f
1
d
a
c
b
g
1
f
f
f
f
d
0
g
a
d
g
a
0
The reduced table has six states, and will require 3 bits of state.
In the state assignment process, r = 3.