Overview. Design Example: Automobile Lock

Transcription

1 Overview Last Lecture: What is the course all about & why is it important? What is a digital system? What is a binary digital system? Boolean lgebra, Truth tables Operators: inversion, and, or, xor, xnor (eq) esign xample: Translating a word problem to a combinational logic function Multiplexers, Implementing the example using a multiplexer This Lecture: esign xample: Translating a word problem into a sequential design language Transition Graph Transition Table Mealy and Moore Forms S5 Newton/Pister.2. esign xample: utomobile Lock The automobile theft rate in Muldavia is so high that yclespersecond rental car agency has decided to add a new security device to their cars. The initial system design has been completed and our consulting firm has been retained to implement the device. The agency designers hand us the following description: "Please build us a small black box (2"x3"x.5") we can attach to the dash that consists of a keypad (keys -9) and two Ls, one green and one red. It should perform as follows: When the ignition is turned on, the red L should light up and the keypad is activated. However, the car will not start. If the driver enters a correct four-digit code, the green L goes on as well and the car can now be started by turning the ignition switch further clockwise to the start position. If the code is not correct, the green light will not go on and the car will not start." S5 Newton/Pister.2.2 S5 Spring 98, opyright 998. Richard Newton, Kris Pister

2 Where o We Start? Write down the inputs and outputs and list the (symbolic) values they can take. hoose a "language" in which to express the behavior of the machine. Is a truth table sufficient here? How would you use it? For sequential systems, we will start by using state transition tables or state transition graphs. We will be assuming discrete-valued time - "instant" to "instant." t any particular instant, the finite number of storage elements in the machine will have particular, welldefined values stored in them - we will be describing problems which can be implemented directly with a Finite- Machine. S5 Newton/Pister.2.3 Naming the Variables R G 2 3 Inputs: Ignition: {off, on, start} Keypad: {,,9} off on keypad Outputs: Red Light: {on, off} Green Light: {on, off} Startar: {yes, no} ignition start What else do we need? Internal state (memory, store, what s happened up until now?, where are we? S5 Newton/Pister.2.4 S5 Spring 98, opyright 998. Richard Newton, Kris Pister 2

3 lements of a Finite- Machine ignition keypad Logic Network Summary so far R G S5 Newton/Pister.2.5 lements of a Finite- Machine ignition keypad Logic Network Summary so far R G Next S5 Newton/Pister.2.6 S5 Spring 98, opyright 998. Richard Newton, Kris Pister 3

4 New Input ata (sensors) Summary of Where We re at time Tn General Structure of Our Problem at Time Tn PRSNT STT (PS) Logic New Output ata (actions) Summary of Where We Got To NXT STT (NS) Will become PS at Time Tn+ S5 Newton/Pister.2.7 Inputs: Ignition: {off, on, start} Keypad: {,,9} Outputs: Red Light: {on, off} Green Light: {on, off} Startar: {yes, no} What else do we need? Special value for when we don t care what the value of an input (or an output) is. or X or - ncoding the Variables Value: off on start ig Value: 2 3 key Value: off on R Value: no yes start S5 Newton/Pister Value: off on G Input vector: {ig key } output vector: { R G start } notation: input/output example: **** / S5 Spring 98, opyright 998. Richard Newton, Kris Pister 4

5 escribing the Required Behavior ig key / R G start Reset state **** / S **** / S S5 Newton/Pister.2.9 hoosing a Language to Represent the Problem We need a "language" to represent: () The of the machine (2) For each possible input value: (2a) The corresponding output value(s) (2b) The corresponding Next S Transition Input Input2 S Output Output2 S2 Next after the value Input is applied Output value(s) after the value Input is applied Output value(s) after the value Input2 is applied Next after the value Input2 is applied S5 Newton/Pister.2. S5 Spring 98, opyright 998. Richard Newton, Kris Pister 5

6 escribing the Required Behavior ig key / R G start Reset state **** / S **** / / S Key on / S 2 S 5 ar started! S 3 S 4 **** / / S 4 / orrect: 23 S5 Newton/Pister.2. xample Finite- Machine Transition iagram (Mealy) Symbolic Inputs / Outputs / / / B / / / / / / / S5 Newton/Pister.2.2 S5 Spring 98, opyright 998. Richard Newton, Kris Pister 6

7 xample Finite- Machine Transition Table (Mealy) Input B Next B Output Next Output S5 Newton/Pister.2.3 escribing the Required Behavior ig key / R G start Reset state **** / S **** / **** /? / / S 2 S * **** / **** / S 5 **** / S 3 S 4 **** / / S 4 / orrect: 23 S5 Newton/Pister.2.4 S5 Spring 98, opyright 998. Richard Newton, Kris Pister 7

8 lements of a Finite- Machine ignition keypad Logic Network R G Next Summary so far : {S, S, S 2, S N } Require Ølog 2 Nø bits of storage to represent the state S5 Newton/Pister.2.5 Finite- Machines Inputs (PIs) Next- Logic Outputs (POs) Latches Mealy Machine S5 Newton/Pister.2.6 S5 Spring 98, opyright 998. Richard Newton, Kris Pister 8

9 xample Finite- Machine ncoded s (Mealy) / / / / B / / / / / / / / / / / / / / / / S5 Newton/Pister.2.7 xample Finite- Machine Next- Logic (Mealy) Inputs... Input Output... Outputs Next S5 Newton/Pister !... S5 Spring 98, opyright 998. Richard Newton, Kris Pister 9

10 xample Finite- Machine Next- Logic (Mealy) in ps(3)' ps()' ps(2) ps(2)' ns() ns(2) ns(3) out in' ps() S5 Newton/Pister.2.9 Finite- Machines Inputs (PIs) Next- Logic Latches Output Logic Outputs (POs) Moore Machine S5 Newton/Pister.2.2 S5 Spring 98, opyright 998. Richard Newton, Kris Pister

11 xample Finite- Machine Transition iagram (Moore) Symbolic Outputs Inputs B S5 Newton/Pister.2.2 xample Finite- Machine Transition Table (Moore) Input B Next B Output S5 Newton/Pister.2.22 S5 Spring 98, opyright 998. Richard Newton, Kris Pister

12 lements of a Finite- Machine ignition keypad Logic Network R G Q LK Q LK Q LK ata () latches Next S5 Newton/Pister.2.23 S5 Spring 98, opyright 998. Richard Newton, Kris Pister 2