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Finite State Machine Example
A Gray-Code Counter
A Finite State Machine Example
• Gray
-
Code
Changes one bit at a time
0 1 3 2
6 7 5 4
12 13
15 14
10 11
9 8
• Reset
true:
register reset to 0 count (synchronous reset)
• Input
I false (and Reset false):
output holds its value
• Input
I true (and Reset false):
register counts up, according to clock
-
wraps from maximum count back to 0
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FSM choices
• simplistic:
separate state for each count
-
n bits  2n states
transitions depend on inputs
Mealey machine? Moore machine?
• two-stage:
FSM keeps track of transitions, output device
keeps track of the actual count
-
Mealey machine? Moore machine?
Simplistic
•3
bits: 23 == 8 counts
-
0 1
-
8 states
»
3 2
6 7
5 4
one per count
• State
bits
are the
outputs
1
3
0
2
4
6
5
7
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Simplistic: transitions
•3
bits: 23 == 8 counts
-
0 1
-
8 states
»
3 2
6 7
5 4
one per count
states at the
clock edge, when the
input I is true
Reset = 1
• Change
I=0
1
I=0
I=0
I=1
3
I=1
I=0
I=1
0
I=1
• “Reset”
input forces
change to state 0 at
the clock edge
2
4
I=1
I=1
I=0
I=0
I=0
5
I=0
I=1
7
6
I=1
Simplistic: implementation
• FSM
-
• How
-
many registers?
Encoded approach: log2(8) == 3 state bits
»
-
design
Registers hold the current state
Combinational logic computes the next state
8 flip-flops, a.k.a. 4-bit register (one bit unused)
One-hot approach: separate flip-flop for each state
»
exactly one flip-flop at a time has output 1
• Output
-
logic
Combinational logic to generate the outputs is trivial!
The state bits represent the counter value
»
encoded state bits are better suited to this
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State
0
1
2
3
4
5
6
7
s2
0
0
0
0
1
1
1
1
s1
0
0
1
1
0
0
1
1
s0
0
1
0
1
0
1
0
1
State
0
1
2
3
4
5
6
7
Reset
I
Next
state
0
0
0
0
1
1
1
-
0
0
0
1
0
1
3
1
-
0
0
0
2
0
1
6
1
-
0
0
0
3
0
1
2
1
-
0
0
0
4
0
1
0
1
-
0
0
0
5
0
1
4
1
-
0
0
0
6
0
1
7
1
-
0
0
0
7
0
1
5
1
-
0
Reset
I
Next
state
n2
n1
n0
0
0
0
0
0
0
0
1
1
0
0
1
1
-
0
0
0
0
0
0
1
0
0
1
0
1
3
0
1
1
1
-
0
0
0
0
0
0
2
0
1
0
0
1
6
1
1
0
1
-
0
0
Reset 0= 1
0
0
0
3
0
1
1
0
1
2
0
1
0
1
-
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
1
-
0
0
0
0
5
1
0 I=1 0
0
1
0
1
4
1
0
0
1
-
0
0
0
0
0
0
6
1
1
0
0
1
7
1
1
1
1
-
0
0
0
0
0
0
7
1
1
1
0
1
5
1
0
1
1
-
0
0
0
0
State Transition
Table
Reset = 1
I=0
1
I=0
I=0
I=1
3
I=1
I=0
I=1
0
I=1
2
4
I=0
5
I=1
I=1
I=0
I=0
6
I=0
I=1
I=1
7
Encode the
States
I=0
1
I=0
I=0
I=1
3
I=1
I=0
I=1
0
2
4
I=1
I=1
I=0
I=0
I=0
5
I=0
I=1
7
6
I=1
4
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