1. CS M51A/EE M16 Winter’05 Section 1 Logic Design of Digital Systems Lecture 16
March 14
W’05
Yutao He
4532B Boelter Hall

2. Outline Administrative Matters Recap
Registers
Shift Registers
Chapter 11 – Sequential macro modules
Counters

3. Administrative Matters
HW# 9
Is posted and will be self-graded
Describes how the topics in Ch. 11 and 12 will be tested
The Final
Is given on Friday
A review session will be held on Wednesday
Extra office hours will be scheduled
My office hours this week
Monday and Wednesday
6-7:30pm
Thursday
7:30-9pm
Graded work

4. Chapter 11 Sequential Modules
Sequential Systems
Flip-Flops
(D, JK, SR, T FFs, etc.)
Chapters 7-8
Design
Analysis
Module networks
(Register, Shift Register, Counter)
Chapter 11
Basic Questions:
What are each module’s property?
inputs, outputs, functions (high-level and binary level)
How to implement it using FFs and logic gates?
How to design a sequential system using these modules?
How to analyze a sequential system using these modules?

5. n-Bit Register

6. Shift Registers Basic Types: Serial In/Serial Out (SI/SO): m=n=1
CLK
Shift Register
CTL n
Basic Types:
Serial In/Serial Out (SI/SO): m=n=1
Serial In/Parallel Out (SI/PO): m=1, n> 1
Parallel In/Serial Out (PI/SO): m>1, n=1
Parallel In/Parallel Out (PI/PO): m, n > 1

7. Modulo-p Counter
Modulo-p Counter
CLK
CTL n TC

8. Modulo-p Counter: High-Level Spec

9. Types of Modulo-p Counter
Sequencing direction
Up counter
Down counter
Up/Down counter
Number of states or Encoding scheme
Binary counter
Decimal (a.k.a. Decade) counter
non-power-of-2 counter
Gray code counter
Ways of implementation
Ring counter
Twisted tail (a.k.a. Johnson, Mobius) counter
Ripple counter

10. Types of Modulo-p Counters (Cont’d)
According to numbers and encoding scheme of states:
Decimal

11. Types of Modulo-p Counters (Cont’d)
Modulo-4 Ring
Counter
Modulo-8
Twisted Tail
Counter

12. Self-Starting Counter
The problem:
Given a counter that does not use all state combinations of the storage elements, how to initialize a counter with a valid state?
The concept of self-starting:
From any initial state, a counter can eventually enter the valid counter sequence.
Example: A modulo-5 counter
111
001
100
110
101
000
010
011
111
001
100
110
101
000
010
011
Self starting
Not Self starting

13. Binary Mod-16 Counter with Parallel Input

14. Binary Counter: High-Level Spec

15. Applications of Counters (1)
Count number of occurrence of an event

16. Applications of Counters (2)
Control a fixed sequence of actions

17. Applications of Counters (3)
Generate timing signals

18. Applications of Counters (4)
Generate clocks of different frequencies

19. Network of Counters Basic approaches of interconnection
Cascade counters
To get longer period
Parallel counters
To get more states

20. Cascade Counters

21. Parallel Counters Design a modulo-504 counter 504=7x8x9
000, 111, 222, 333, 444, …

22. Design Using Binary Counters
Typical Problems:
Given a modulo-p counter, implement:
modulo-k (up) counter, where 1  k  p
a-to-b counter, where 1  a < b  p
modulo-k down counter
up/down modulo-k counter
any sequential systems
Basic approach:
Try to design the “glue logic” around the basic counter:
How to perform initialization
How to detect a state
How to skip a state

23. Binary Modulo-16 Counter
CLK LD TC
I I2 I1 I0
S3 S2 S1 S0
CNT
CLR

24. Design with Modulo-16 Counter• s 4 • • x I 4 • •

25. Design A Modulo-12 Counter
CLK LD
I I2 I1 I0
S3 S2 S1 S0
CNT
CLR x S0 S1 S3 TC

26. Design A 1-to-12 Counter S3 S2 S1 S0 CLR x CNT Modulo-16 Counter CLKLD
I I2 I1 I0
S3 S2 S1 S0
CNT
CLR x S2 S3 TC

27. Design A Modulo-16 Down Counter
The key observation:
Each next state needs to be loaded from parallel inputs I3,I2,I1,I0 when count input is 1.
Modulo-16 Counter
CLK LD
I I2 I1 I0
S3 S2 S1 S0
CNT
CLR x
Comb. Logic
TC(-)
S3 S2 S1 S0 x

28. A Modulo-16 Down Counter - Cont.
Function Table:
Inputs: S3, S2, S1, S0, and x
Outputs: I3,I2,I1,I0, and TC(-)
S3 S2 S1 S0 I3 I2 I1 I0 TC(-)
x = 0
S3 S2 S1 S0 I3 I2 I1 I0 TC(-)
x = 1
What about a Modulo-12 down counter?

29. Design A Up/Down Modulo-16 Counter
Need to introduce mode control inputs:
(x,y)=(1,0)  Up
(x,y)=(0,1)  Down
x = y, do not change
Modulo-16 Counter
CLK LD
I I2 I1 I0
S3 S2 S1 S0
CNT
CLR x y
x y
Comb. Logic
TC(+)
TC(-)
S3 S2 S1 S0
x’y

30. Design Any Sequential Systems
Key steps:
Obtain the transition tables
Design the combinational logic

31. Example 1
Using a modulo-16 counter, implement a counter with the following periodical sequence:
0, 2, 5, 6, 7, 9, 10, 12, 13, 15
Modulo-16 Counter
CLK LD
I I2 I1 I0
S3 S2 S1 S0
CNT
CLR x
Comb. Logic TC
S3 S2 S1 S0 x

32. Example - Cont. x = 0 x = 1 S3 S2 S1 S0 I3 I2 I1 I0 TC

33. Summary
Chapter 11
Counter

34. Next Lecture
Chapter 12 - ROM
Final Review
Course Evaluation