1. Dr. Clincy Professor of CS
CS Chapter 3 (3A and )
Dr. Clincy
Professor of CS
Exam 2 and 3 Overview and Logistics
Final Project Rollout
Lab 6
Dr. Clincy
Lecture
Slide 1 1

2. Exam 2 and Exam 3
Exam 2 (Thursday, June 28th) – Closed Book – focuses on Ch 3’s Boolean Algebra
Can work on final project after exam until 630pm
Lecture 15 will be posted online
Exam 3 (Tuesday, July 3rd) – Open Book No Laptop – focuses on Ch 3’s circuits
Lab after exam
Can work on final project after lab until 630pm
Lecture 16 will be posted online
Dr. Clincy
Lecture
Slide 2 2

3. Sequential Circuits Vs Combinational Circuits
Sequential Logic
Current State or output of the device is affected by the previous states
Circuit
Flip Flops
New Input
Previous State or Output
Current State or Output
Combinatorial or Combinational Logic
Circuit
New Input
Current State or Output
Current State or output of the device is only affected by the current inputs
Dr. Clincy
Lecture

4. Clock - Sequential Circuits
State changes are controlled by clocks (clock ticks).
Circuits can change state on the rising edge, falling edge, or when the clock pulse reaches its highest voltage – edge triggered.
Level-triggered circuits change state when the clock voltage reaches its highest or lowest level.
Dr. Clincy
Lecture

5. Flip Flops - Sequential Circuits
New Input
Previous State or Output
Current State or Output
Notice how the output feeds the input
Think of: Given R=0 and Qa=0, what can this be ?
S and R stand for set and reset respectively
constructed from a pair of cross-coupled NOR gates
the stored bit is present on the output marked Qa
If S and R inputs are both low, maintains the Qa and Qb in constant state,
If S (Set) is pulsed high while R is held low, then the Qa output is forced high,and stays high even after S returns low;
if R (Reset) is pulsed high while S is held low, then the Qa output is forced low, and stays low even after R returns low.
Dr. Clincy
Lecture

6. Gated SR Latch or Flip Flop
The time at which the latch is SET or RESET is controlled by a CLOCK input
Called Gated SR Latch
Dr. Clincy
Lecture

7. Gated D Latch Inputs S and R are derived from a single input D
Clock pulse controls when the output is triggered
Samples the D input at the time the clock is HIGH and stores that info until the next clock pulse
During the time the clock is high, the input changed, causing the output to change – this is the problem
Dr. Clincy
Lecture

8. Potential Problem
Thus far, the assumption has been the inputs S and R (or D) not changing while CLK is HIGH
What would happen if S, R and/or D changed ? The output would change immediately
This could be a problem
To fix this (next ppt)
During the time the clock is high, the input changed, causing the output to change – this is the problem
Dr. Clincy
Lecture

9. Two Flip Flop Use To Fix Clock Issue
FF1
FF2 Q Q D D Q m D Q s Q
Clock
Clk Q
Clk Q Q
Use 2 D flip flops – the FF2 clock is set to zero – therefore, if there was a change in FF1 input, D, it wouldn’t effect the FF2 Q value – FF2 holds the value
(a) Circuit
Clock D Q m Q = Q s
Clock’s negative edge causes change
(b) Timing diagram
If D changes while FF1 CLK is HIGH, Qm changes immediately - Qs stays the same because FF2 CLK=0
Once the CLK goes LOW, FF2 reacts because its CLK=1 – so it thens reflects D D Q
The arrow only symbolizes “positive edge” clock - the arrow with the NOT symbolizes “negative edge” clock Q
(c) Graphical symbol
Dr. Clincy
Lecture

10. T Flip Flop
T Flip Flops are good for counters – changes its state every clock cycle, if the input, T, is 1
Positive-edge triggered flip flop
Since the previous state of Q was 0, it complements it to 1
Dr. Clincy
Lecture

11. JK Flip Flop Combines the behavior of the SR and T flip flops
First three entries are the same behavior as the SR Latch (when CLK=1)
Usually the state S=R=1 undefined – for the JK Flip Flop, for J=K=1, next state is the complement of the present state
Can store data like a D Flip Flop or can tie J & K inputs together and use to build counters (like a T flip flop)
Dr. Clincy
Lecture

12. Registers and Shift Registers
A Flip Flop can store ONE bit – in being able to handle a WORD, you will need a number of flip flops (32, 64, etc) arranged in a common structure called a REGISTER.
All flip flops are synchronized by a common clock
Data written into (loaded) flip flops at the same time
Data is read from all flip flops at the same time F F F F 1 2 3 4 In D Q D Q D Q D Q
Out
Clock Q Q Q Q
A simple shift register.
Want the ability to rotate and shift the data
Clock pulse will cause the contents of F1, F2, F3 and F4 to shift right (serially)
To do a rotation, simply connect OUT to IN
Dr. Clincy
Lecture

13. Registers and Shift Registers
Can load either serially or in parallel
When clock pulse occurs,
Serial shift takes place if Shift’/Load=0 or
if Shift’/Load=1, parallel load is performed
Dr. Clincy
Lecture

14. Counters Hmmm Called a Ripple Counter
3-stage or 3-bit counter constructed using T Flip Flops
With T Flip Flips, when input T=1, the flip flop toggles – changes state for each successive clock pulse
Initially all set to 0
When clock pulse, Q0=1, therefore Q’=0 disabling Q1 and Q1 disables Q2 (have 1,0,0)
For the 2nd clock pulse, Q0=0, therefore Q’=1, causing Q1=1 and therefore Q’=0 disabling Q2 (have 0,1,0)
For the 3rd clock pulse, Q0=1, therefore Q’=0 disabling Q2 and therefore disabling Q3 (have 1,1,0)
Etc….
LSB
000
001
010
011
100
101
110
111
Hmmm
Dr. Clincy
Lecture
Called a Ripple Counter

15. Dr. Clincy Professor of CS
CS Chapter 3 (3A and )
Dr. Clincy
Professor of CS
Dr. Clincy
Lecture
Slide 15 15

16. NOTE Your book doesn’t do a good job in showing you how to derive or design sequential circuits (using state and state assignment tables) – the lecture will do so – please pay close attention to the lecture in understanding how to derive sequential circuits.
You can print out the slides in this lecture only for exam 2 (open book part 2 only). You should NOT add any notes to the printed slides. You will receive a penalty if personal notes are written on the slides
Dr. Clincy
Lecture
Slide 16 16

17. Combinatorial or Combinational Logic
Recall
Circuit
New Input
Current State or Output
Combinatorial or Combinational Logic
Current State or output of the device is only affected by the current inputs
Examples:
Decoders
Multiplexers
Current State or output of the device is affected by the previous states
Circuit
Flip Flops
New Input
Previous State or Output
Current State or Output
Sequential Logic
Examples:
Shift Registers
Counters
Dr. Clincy
Lecture

18. Sequential Circuit – State Diagram
If x=0, count up,
If x=1, count down
Interested when 2 is realized – z=1 when reach 2, else z=0
If at 0 and x=0, count up to 1 (and z=0)
If at 0 and x=1, count down to 3 (and z=0) x = z 1 S2 S3
State diagram of a mod-4 up/down counter that detects the count of 2. S1 S0
State diagram describes the functional behavior without any reference to implementation
Dr. Clincy
Lecture

19. Sequential Circuit – State Table
Can represent the info in the state diagram in a state table x = z 1 S2 S3
State diagram of a mod-4 up/down counter that detects the count of 2. S1 S0
Dr. Clincy
Lecture

20. Sequential Circuit – Equation
Inputs – y2,y1,x
Outputs –Y2, Y1
Dr. Clincy
Lecture

21. Sequential Circuit – Circuit Design
D Flip Flops used to store values of the two state variables between clock pulses
Output from Flip Flops is the present-state of the variables
Input, D, of the Flip Flops is the next-state of the variables
Dr. Clincy
Lecture

22. Finite State Machine Model
The example we just implemented is an example of a “Finite State Machine” - is a model or abstraction of behavior composed of a finite number of states, transitions between those states, and actions
Dr. Clincy
Lecture

23. Final Project Rollout
Lab 6
Dr. Clincy
Lecture
Slide 23 23