Lecture 18 More Moore/Mealy machines.

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Presentation transcript:

Lecture 18 More Moore/Mealy machines

Example: Parity checker Serial input string OUT=1 if odd # of 1s in input OUT=0 if even # of 1s in input Let’s do this for Moore and Mealy

1. State diagram Moore Mealy 0/0 1/1 1/0 0/1

2. State transition table Present Input Next Present State State Output Even 0 Even 0 Even 1 Odd 0 Odd 0 Odd 1 Odd 1 Even 1 Moore Present Input Next Present State State Output Even 0 Even 0 Even 1 Odd 1 Odd 0 Odd 1 Odd 1 Even 0 Mealy

3. State minimization Already minimized Need both states (even and odd) Use one flip-flop

4. State encoding Moore Mealy Present Input Next Present State State Output 0 0 0 0 0 1 1 0 1 0 1 1 1 1 0 1 Assignment Even 0 Odd 1 Moore Present Input Next Present State State Output 0 0 0 0 0 1 1 1 1 0 1 1 1 1 0 0 Mealy

5. Next-state logic minimization Assume D flip-flops Next state = (present state) XOR (present input)

6. Implement the design Moore Mealy CLK Input Current State D Q Output

Example: Vending machine Vending Machine FSM N D Reset Clock Open Coin Sensor Release Mechanism

Moore machine 0¢ Reset 5¢ N N + D 10¢ D 15¢ [open] symbolic state table present inputs next present state D N state output 0¢ 0 0 0¢ 0 0 1 5¢ 0 1 0 10¢ 0 1 1 – – 5¢ 0 0 5¢ 0 0 1 10¢ 0 1 0 15¢ 0 1 1 – – 10¢ 0 0 10¢ 0 0 1 15¢ 0 1 0 15¢ 0 1 1 – – 15¢ – – 15¢ 1

Mealy machine 0¢ Reset 5¢ N/0 N + D/1 10¢ D/0 15¢ D/1 symbolic state table present inputs next present state D N state output 0¢ 0 0 0¢ 0 0 1 5¢ 0 1 0 10¢ 0 1 1 – – 5¢ 0 0 5¢ 0 0 1 10¢ 0 1 0 15¢ 1 1 1 – – 10¢ 0 0 10¢ 0 0 1 15¢ 1 1 0 15¢ 1 1 1 – – 15¢ – – 15¢ 1

Moore machine: State encoding symbolic state table present inputs next present state D N state output 0¢ 0 0 0¢ 0 0 1 5¢ 0 1 0 10¢ 0 1 1 – – 5¢ 0 0 5¢ 0 0 1 10¢ 0 1 0 15¢ 0 1 1 – – 10¢ 0 0 10¢ 0 0 1 15¢ 0 1 0 15¢ 0 1 1 – – 15¢ – – 15¢ 1 present state inputs next state present Q1 Q0 D N D1 D0 output 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 1 1 – – – 0 1 0 0 0 1 0 0 1 1 0 0 1 0 1 1 0 1 1 – – – 1 0 0 0 1 0 0 0 1 1 1 0 1 0 1 1 0 1 1 – – – 1 1 – – 1 1 1

Mealy machine: State encoding symbolic state table present inputs next present state D N state output 0¢ 0 0 0¢ 0 0 1 5¢ 0 1 0 10¢ 0 1 1 – – 5¢ 0 0 5¢ 0 0 1 10¢ 0 1 0 15¢ 1 1 1 – – 10¢ 0 0 10¢ 0 0 1 15¢ 1 1 0 15¢ 1 1 1 – – 15¢ – – 15¢ 1 present state inputs next state present Q1 Q0 D N D1 D0 output 0 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 0 1 1 – – – 0 1 0 0 0 1 0 0 1 1 0 0 1 0 1 1 1 1 1 – – – 1 0 0 0 1 0 0 0 1 1 1 1 1 0 1 1 1 1 1 – – – 1 1 – – 1 1 1

Logic minimization Moore Mealy 0 0 1 1 0 1 1 1 X X X X 1 1 1 1 Q1 D1 0 0 1 1 0 1 1 1 X X X X 1 1 1 1 Q1 D1 Q0 N D Moore 0 0 1 0 0 0 1 0 X X 1 X 0 0 1 0 Q1 Open Q0 N D 0 1 1 0 1 0 1 1 X X X X 0 1 1 1 Q1 D0 Q0 N D Mealy 0 0 1 1 0 1 1 1 X X X X 1 1 1 1 Q1 D1 Q0 N D 0 0 1 0 0 0 1 1 X X 1 X 0 1 1 1 Q1 Open Q0 N D 0 1 1 0 1 0 1 1 X X X X 0 1 1 1 Q1 D0 Q0 N D

Implementation Moore Mealy

7.24 A Moore machine has two inputs (X1, X2) and one output (Z). The output remains a constant value unless one of the following input sequence occurs: The input sequence 00,11 causes the output to become 0. The input sequence 01,11 causes the output to become 1. The input sequence 10,11 causes the output to toggle value.

7.23 A Mealy machine has one input (X) and two outputs (Z1 and Z2). An output Z1 = 1 occurs every time the input sequence 101 is observed, provided the sequence 011 has never been seen. An output Z2 = 1 occurs every time the input 011 is observed.