mealy and moore machines
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Mealy and Moore Machines
Mealy Machines
State TablePresent State Next State Output
X=0 X=1 X=0 X=1
S0 S1 S0 0 0
S1 S1 S2 0 0
S2 S1 S0 1 0
STATE ASSIGNMENT1.Pair the present state for which the next state is same for X=0 and X=12.Pair the next state for the present state. For eg: for S0 the next states would be S1 and S2. Hence pair of (1,2) will be formed. 3.Pair the present states for which the output value is equal to 1
State Assignment• According to the State assignment rules, pairs formed will be:• 1. For X=0, (0,1,2) and for X=1 (0,2) will be paired• 2. no pairing is possible• 3. (2) single pair
• S0 = 00• S1 = 10• S2 =01
0 1
0 S0 S1
1 S2 --
Q1
Q2
State tablePresent state Next State Output (z)
X=0 X=1 X=0 X=1
Q1 Q2 Q1+ Q2+ Q1+ Q2+
0 0 1 0 0 0 0 0
1 0 1 0 0 1 0 0
0 1 1 0 0 0 1 0
Now solve for Q1+ and Q2+ and output z using K maps.
K map Solution• For Q1+
• Q1 Q2 00 01 11 10
X 0 Q1+ = X
1
• For Q2 + Q1 Q2
00 01 11 10 Q2+ = X Q1X 0
1
1 1 x 1
x
X
x 1
Output and hardware implementation
• Value of output z = Q1Q2 00 01 11 10X 0
1Z= X Q2
X
1 x
Hardware implementation
D1 Q1
Q1
D2 Q2
Q2
Moore Machines• Output depends only upon the present state not on the
inputs. Pattern to be detected: 010 X=1
(1 is stored)
X=1 X=0 X=0X=1
X=0 (0 is stored)(010 is stored)
X=0 X=1(01 is stored)
S00
S10
S20
S31
State Table • 4 states are used.
• Assignment of States1. (0,1) and (0,2)2. 3. (3)
Present State Next State OutputX=0 X=1 X=0/1
S0 S1 s0 0
S1 S1 S2 0
S2 S3 S0 0
S3 S1 S0 1
K Map
• Assignment of states Q1 0 1 S0 : 00
Q2 0 S1 : 101 S2 : 01
S3 : 11
S0 S1
S2 S3
State table Present state Next State
X=0 X=1Output(z)
Q1 Q2 Q1+ Q2+ Q1+ Q2+
0 0 1 0 0 0 0
1 0 1 0 0 1 0
0 1 1 1 0 0 0
1 1 0 0 1 0 1
Solution for Q1+ and Q2+
• Q1+ : Q1Q2 00 01 11 10 X 0
1 D1 = X Q2 + X Q1 + X Q1 Q2• Q2+ :
D2 = X Q1 Q2 + X Q1 Q2
1 1 1
1
1
1
Solution for K map
Since it is the moore machine only at the state output shall be equal to 1 and ‘Z’ is independent of input variable ‘X’. Z = Q1 Q2
Hardware Implementation