CEC 220 Digital Circuit Design Sequence Detector Design Wednesday, April 01 CEC 220 Digital Circuit Design Slide 1 of 11.

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CEC 220 Digital Circuit Design Sequence Detector Design Wednesday, April 01 CEC 220 Digital Circuit Design Slide 1 of 11

Lecture Outline Wednesday, April 01 CEC 220 Digital Circuit Design More Sophisticated Sequence Detector Design Incompletely Specified State Graph Boolean State Graph Notation Slide 2 of 11

Sequence Detector Design More Sophisticated Sequence Detector Wednesday, April 01 CEC 220 Digital Circuit Design Develop a sequence detector which asserts its output (Z) if either a “010” or “1001” is detected on the serial input (X)  How should the state machine respond to  X= 0,0,1,0,1,0,0,1,0,0,1,…  Z=  Develop the state graph for a Moore machine solution  Develop the state graph for a Mealy machine solution 0,0,0,1,0,1,1,0,1 Slide 3 of 11

Incompletely Specified State Graphs Wednesday, April 01 CEC 220 Digital Circuit Design Design a Vending Machine  Dispense a stick of gum when 15 ¢ or more is collected and then return to “start”  Accept a single nickel or dime at a time  No change is provided BLOCK DIAGRAM Example behavior: N: 0,1,0,0,0,0,… D: 0,0,1,0,1,1,… Assumption: System clock is “high speed” Assumption: System clock is “high speed” Coin Sensor Vending Machine Gum Dispenser N D Z ClkReset Z: 0,0,1,0,0,1,… Slide 4 of 11

Incompletely Specified State Graphs Wednesday, April 01 CEC 220 Digital Circuit Design State Graph  Moore Machine 00 State Name Output Legend : Input=ND S 0¢ 0 RESET S5 ¢ 0 10 S10 ¢ 0 10 S15 ¢ , 01, Present State Next StatePresent Output (Z) ND=00ND=01ND=10ND=11 S 0¢ S 5¢ S1 0¢ S 15¢ Present State Next StatePresent Output (Z) ND=00ND=01ND=10ND=11 S 0¢ 0 S 5¢ 0 S1 0¢ 0 S 15¢ 1 Present State Next StatePresent Output (Z) ND=00ND=01ND=10ND=11 S 0¢ S1 0¢ S 5¢ X 0 S1 5¢ S 10¢ X 0 S1 5¢ X 0 S0 ¢ X 1, 01 The state graph is incompletely specified!! The state graph is incompletely specified!! Slide 5 of 11

Incompletely Specified State Graphs Wednesday, April 01 CEC 220 Digital Circuit Design Circuit design (D-type flip-flops) Present State Next StatePresent Output (Z) Flip-Flop Inputs (D A D B ) S 0¢ S1 0¢ S 5¢ X0 S1 5¢ S 10¢ X0 S1 5¢ X0 S0 ¢ X1 QAQBQAQB S 0¢ = 00 S 5¢ = 01 S1 0¢ = 10 S15 ¢ =11 State Encodings Present Output (Z) Flip-Flop Inputs (D A D B ) XX XX XX XX1 Present Output (Z) Flip-Flop Inputs (D A D B ) XX XX XX XX XX01011 XX 1100 XX100 XX X0 0101X1 1100X0 1011X X1 0111X0 1100X0 1001X1 Slide 6 of 11

Incompletely Specified State Graphs Wednesday, April 01 CEC 220 Digital Circuit Design State Graph  Mealy Machine 00/0 State Name Legend : Input / Output (ND) S 0¢ RESET S5 ¢ 10 /0 S10 ¢ 10 /0 10/1 00/0 01/0 Present State Next StatePresent Output (Z) S 0¢ S 5¢ S1 0¢ The state graph is incompletely specified!! The state graph is incompletely specified!! 01/1 Present State Next StatePresent Output (Z) S 0¢ 000X S 5¢ 010X S1 0¢ 011X Present State Next StatePresent Output (Z) S 0¢ S1 0¢ S 5¢ X000X S 0¢ S1 0¢ X010X S 0¢ X011X Slide 7 of 11

Incompletely Specified State Graphs Wednesday, April 01 CEC 220 Digital Circuit Design Circuit design (D-type flip-flops) QAQBQAQB S 0¢ = 00 S 5¢ = 01 S1 0¢ =10 State Encodings X0 0100X1 11XXXX 1010X X1 0110X0 11XXXX 1000X0 Present State Next StatePresent Output (Z)Flip-Flop In (D A D B ) S 0¢ S1 0¢ S 5¢ X000X S 0¢ S1 0¢ X010X S 0¢ X011X Present State Next StatePresent Output (Z)Flip-Flop In (D A D B ) XX000X XX010X XX011X 11XX Present State Next StatePresent Output (Z)Flip-Flop In (D A D B ) XX000X001001XX XX010X010010XX XX011X1000 XX 11XX XXXX X0 0101X0 11XXXX 1001X1 Slide 8 of 11

Boolean State Graph Notation Wednesday, April 01 CEC 220 Digital Circuit Design Recall the Moore Machine Chart 00 State Name Output Legend : Input=ND S 0¢ 0 RESET S5 ¢ 0 10 S10 ¢ 0 10 S15 ¢ , 01, 10, 01 NDND RESET S15 ¢ Z Boolean State Graph Notation Slide 9 of 11

Boolean State Graph Notation Wednesday, April 01 CEC 220 Digital Circuit Design Recall the Mealy Machine Chart 00/0 S 0¢ RESET S5 ¢ 10 /0 S10 ¢ 10 /0 10/1 00/0 01/0 01/1 State Name Legend : Input / Output (ND) (Z) S 0¢ S5 ¢ S10 ¢ RESET N  D/Z Slide 10 of 11

Next Lecture Wednesday, April 01 CEC 220 Digital Circuit Design More FSM Examples Slide 11 of 11