![Page 1: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/1.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE3563 Chapter 7, 8, 10 Reading Assignments
7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2, 8.5.4 8.8 10.1, 10.2, 10.3.1-10.3.4, 10.4.1, 10.4.2
![Page 2: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/2.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE3563 Revisit Transfer Curve
![Page 3: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/3.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE 3563 Clocked Synchronous State Machines
A state machine has several components:– Next-State Logic
• Combinational logic that determines what the next state should be
– State Memory• Value of output of flip flops
– Output Logic• Flip flop output is not necessarily the final output• For example, output might be the ANDing of the flip-flop output
Clocked means that transitions only happen on the tick of a clock
Synchronous means that all transitions happen at the same time – the tick of the clock
There are 2n distinct states with n being the number of binary state variables
![Page 4: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/4.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE 3563 Clocked Synchronous State Machines
Mealy machine – output logic takes as input the current state as well as the machine inputs
![Page 5: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/5.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE 3563 Clocked Synchronous State Machines
Moore machine – output logic is solely based upon the current state
If some outputs depend on inputs and some don’t, then it is classified as a Mealy machine
![Page 6: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/6.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE 3563 Clocked Synchronous State Machines
Outputs may be pipelined as well, that is, the final outputs depend upon the state and inputs of the previous clock period
Pipelining can be very efficient, much like an assembly line When a machine has multiple stages, pipelining can allow
each stage to work in parallel thereby increasing efficiency
![Page 7: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/7.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE 3563 Clocked Synchronous State Machines
The functional behavior of a latch or flip-flop can be described with a characteristic equation
It specifies the next state as a function of inputs and current state
![Page 8: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/8.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE 3563 Clocked Synchronous State Machines
State machine with two positive-edge-triggered D flip-flops
![Page 9: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/9.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE 3563 Clocked Synchronous State Machines
Transition Table, State Table, State/Output Table
![Page 10: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/10.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE 3563 Clocked Synchronous State Machines
State Diagram for D-FF Mealy State Machine
![Page 11: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/11.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE 3563 Clocked Synchronous State Machines
State Diagram for D-FF Moore State Machine
![Page 12: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/12.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE 3563 Clocked Synchronous State Machines
D-FF State Machine Redrawn
![Page 13: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/13.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE 3563 Clocked Synchronous State Machines
Steps for analyzing a clocked synchronous circuit:– Get excitation equations
– Substitute excitation equations into flip-flop characteristic equations
– Use transition equations to construct transition table
– Get output equations
– Create transition/output table
– Name states and substitute state names for state-variable combinations to create state output table
– Draw a state diagram corresponding to the state/output table
The text goes through these steps for a different example on pages 559-560
We will go through the steps, but using the J-K flip-flop example
![Page 14: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/14.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE 3563 Clocked Synchronous State Machines
Get Excitation Equations
![Page 15: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/15.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE 3563 Clocked Synchronous State Machines
Get Excitation Equations
![Page 16: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/16.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE 3563 Clocked Synchronous State Machines
Substitute excitation equations into flip-flop characteristic equations to get transition equations
Characteristic EquationsExcitation Equations
Transition Equations
![Page 17: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/17.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE 3563 Clocked Synchronous State Machines
Use transition equations to construct transition table
![Page 18: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/18.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE 3563 Clocked Synchronous State Machines
Get output equation
![Page 19: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/19.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE 3563 Clocked Synchronous State Machines
Get output equation
Z = X * Q0*Q1 + Y*Q0’*Q1’
![Page 20: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/20.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE 3563 Clocked Synchronous State Machines
Create transition/output table
Transition Output Table
![Page 21: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/21.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE 3563 Clocked Synchronous State Machines
Name states and substitute state names for state-variable combinations to create state output table
State Output Table
![Page 22: Fall 2004EE 3563 Digital Systems Design EE3563 Chapter 7, 8, 10 Reading Assignments 7.1, 7.2, 7.3 8.1, 8.2.1-8.2.3, 8.2.5 8.4.1-8.4.3 8.5.1, 8.5.2,](https://reader036.vdocument.in/reader036/viewer/2022081519/56649f265503460f94c3c791/html5/thumbnails/22.jpg)
Fall 2004 EE 3563 Digital Systems Design
EE 3563 Clocked Synchronous State Machines
Draw a state diagram corresponding to the state/output table