ECED2200 Digital Circuits Counters 24/07/2012 Colin OFlynn - CC - PowerPoint PPT Presentation

ECED2200 – Digital Circuits Counters 24/07/2012 Colin O’Flynn - CC BY-SA 1

General Notes See updates to these slides: www.newae.com/teaching • These slides licensed under ‘Creative Commons Attribution-ShareAlike 3.0 • Unported License’ These slides are not the complete course – they are extended in-class • You will find the following references useful, see • www.newae.com/teaching for more information/links: The book “Bebop to the Boolean Boogie” which is available to Dalhousie Students – Course notes (covers almost everything we will discuss in class) – Various websites such as e.g.: www.play-hookey.com – The book “Contemporary Logic Design”, which was used in previous iterations of the – class and you may have already 24/07/2012 Colin O’Flynn - CC BY-SA 2

DIVIDE-BY N COUNTER 24/07/2012 Colin O’Flynn - CC BY-SA 3

Divide-By N CLK/2 CLK/4 CLK/8 CLK 24/07/2012 Colin O’Flynn - CC BY-SA 4

CLK/4 Divide-By N CLK/2 CLK 24/07/2012 Colin O’Flynn - CC BY-SA 5

Uses of Divide-By-N 32.768 KHz crystal 24/07/2012 Colin O’Flynn - CC BY-SA 6

Uses of Divide-By-N 32.768 KHz crystal 2 15 = 32768 24/07/2012 Colin O’Flynn - CC BY-SA 7

BINARY RIPPLE COUNTER 24/07/2012 Colin O’Flynn - CC BY-SA 8

Binary Ripple Design 24/07/2012 Colin O’Flynn - CC BY-SA 9

Up Counter Q0 Q1 Q3 CLK 24/07/2012 Colin O’Flynn - CC BY-SA 10

Down Counter Q0 Q1 Q3 CLK 24/07/2012 Colin O’Flynn - CC BY-SA 11

SYNCHRONOUS COUNTER 24/07/2012 Colin O’Flynn - CC BY-SA 12

24/07/2012 Colin O’Flynn - CC BY-SA 13

Count Sequence? 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 24/07/2012 Colin O’Flynn - CC BY-SA 14

Synchronous Counter Design 24/07/2012 Colin O’Flynn - CC BY-SA 15

RING COUNTER 24/07/2012 Colin O’Flynn - CC BY-SA 16

Design 24/07/2012 Colin O’Flynn - CC BY-SA 17

DESIGN PROCEDURE FOR ARBITRARY COUNTERS 24/07/2012 Colin O’Flynn - CC BY-SA 18

Design Specs 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0 (0, 2, 3, 5, 6) 24/07/2012 Colin O’Flynn - CC BY-SA 19

Procedure 1. Draw state transition diagram 2. Write state transition table 3. Choose flip-flops & determine required inputs 4. Design logic to realize required inputs 24/07/2012 Colin O’Flynn - CC BY-SA 20

Counter Design Example 0 0 0 0 1 0 0 1 1 1 0 1 1 1 0 (0, 2, 3, 5, 6) 24/07/2012 Colin O’Flynn - CC BY-SA 21

1. State Transition Diagram 110 000 010 101 011 24/07/2012 Colin O’Flynn - CC BY-SA 22

2. State Transition Table A + B + C + A B C 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 24/07/2012 Colin O’Flynn - CC BY-SA 23

2. State Transition Table A + B + C + A B C 0 0 0 0 1 0 0 0 1 ? ? ? 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 ? ? ? 1 0 1 1 1 0 1 1 0 0 0 0 1 1 1 ? ? ? 24/07/2012 Colin O’Flynn - CC BY-SA 24

3. Select Flip-Flop e.g.: We will use T flip-flops: Q Q+ T 0 0 0 0 1 1 1 0 1 1 1 0 24/07/2012 Colin O’Flynn - CC BY-SA 25

Q Q+ T 0 0 0 3. Figure out FF Inputs 0 1 1 1 0 1 1 1 0 A + B + C + A B C TA TB TC 0 0 0 0 1 0 0 0 1 ? ? ? 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 ? ? ? 1 0 1 1 1 0 1 1 0 0 0 0 1 1 1 ? ? ? 24/07/2012 Colin O’Flynn - CC BY-SA 26

Q Q+ T 0 0 0 3. Figure out FF Inputs 0 1 1 1 0 1 1 1 0 A + B + C + A B C TA TB TC 0 0 0 0 1 0 0 1 0 0 0 1 ? ? ? ? ? ? 0 1 0 0 1 1 0 0 1 0 1 1 1 0 1 1 1 0 1 0 0 ? ? ? ? ? ? 1 0 1 1 1 0 0 1 1 1 1 0 0 0 0 1 1 0 1 1 1 ? ? ? ? ? ? 24/07/2012 Colin O’Flynn - CC BY-SA 27

4. Generate Required Logic A B C TA 0 0 0 0 0 0 1 ? 0 1 0 0 0 1 1 1 1 0 0 ? 1 0 1 0 1 1 0 1 1 1 1 ? 24/07/2012 Colin O’Flynn - CC BY-SA 28

4. Generate Required Logic A B C TB 0 0 0 1 0 0 1 ? 0 1 0 0 0 1 1 1 1 0 0 ? 1 0 1 1 1 1 0 1 1 1 1 ? 24/07/2012 Colin O’Flynn - CC BY-SA 29

4. Generate Required Logic A B C TC 0 0 0 0 0 0 1 ? 0 1 0 1 0 1 1 0 1 0 0 ? 1 0 1 1 1 1 0 0 1 1 1 ? 24/07/2012 Colin O’Flynn - CC BY-SA 30

4. Implement B A C CLK 24/07/2012 Colin O’Flynn - CC BY-SA 31

4. Implement 24/07/2012 Colin O’Flynn - CC BY-SA 32

Verifying if Counters are Self-Starting A + B + C + A B C TA TB TC 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 24/07/2012 Colin O’Flynn - CC BY-SA 33

State Transition Diagram 110 000 010 101 011 24/07/2012 Colin O’Flynn - CC BY-SA 34

More See class notes for lots of examples of creating counters & verifying if they are self-starting or not 24/07/2012 Colin O’Flynn - CC BY-SA 35