1. Sequential circuits and Digital System Reliability
Dr. Konstantinos Tatas

2. ACOE161 - Digital Logic for Computers - Frederick University
Outline
Sequential Circuits
Register
Shift Register
Bidirectional Shift Register with Parallel Load
Counters
Adder-based
Ring Counter
Johnson Counter
Digital System Reliability
What is Reliability
Errors and Faults
Design for Reliability
ACOE161 - Digital Logic for Computers - Frederick University

3. ACOE161 - Digital Logic for Computers - Frederick University
Register
A register is a sequential circuit that stores a word.
It is composed of flip-flops (usually D-type)
ACOE161 - Digital Logic for Computers - Frederick University

4. ACOE161 - Digital Logic for Computers - Frederick University
Shift Register
A register that “shifts” its contents in one direction
Composed of D f/fs chained so that each Q output is connected to the next D input
ACOE161 - Digital Logic for Computers - Frederick University

5. Bidirectional Shift Register with Parallel Load
Inputs:
Clock
Reset
2 Control bits
00: no shift
01: shift right
10: shift left
11: parallel load
Parallel load inputs
Outputs:
Parallel output
ACOE161 - Digital Logic for Computers - Frederick University

6. Bidirectional Shift Register with Parallel Load Circuit Diagram
ACOE161 - Digital Logic for Computers - Frederick University

7. LFSR Linear Feedback Shift Register
Shift register with input taken from XOR of state
Pseudo-Random Number Generator
Step Y
111 1
110 2
101 3
010 4
100 5
001 6
011 7
111 (repeats) Y
Flops reset to 111

8. ACOE161 - Digital Logic for Computers - Frederick University
Counters
Synthesizing a 4-bit up counter from VHDL using the “+” operator will produce this circuit
signal ct: std_logic_vector(3 downto 0);
Begin
ct <= ct + ‘1’;
ACOE161 - Digital Logic for Computers - Frederick University

9. The trouble with adder-based counters
A ripple carry adder becomes too slow for large numbers of bits.
Can use carry look-ahead adder
Use “optimize for speed” in synthesis options
Use JK or T flip-flops (not available in most FPGAs, but you can create one from D F/Fs)
OR you can use the following counters
ACOE161 - Digital Logic for Computers - Frederick University

10. ACOE161 - Digital Logic for Computers - Frederick University
Ring Counter
A shift counter with feedback that is initiated with one f/f in different state than the rest
Total of N states (1-hot counter)
Q0Q1Q2Q3
repeat
ACOE161 - Digital Logic for Computers - Frederick University

11. ACOE161 - Digital Logic for Computers - Frederick University
Johnson Counter
A modification of the ring counter with 2*N states
ACOE161 - Digital Logic for Computers - Frederick University

12. Digital System Reliability

13. What is Reliability?
A digital system is reliable if it always performs according to its specification
Truth table
State diagram
Integrated Circuits are becoming increasingly unreliable
Transistors are so small that are affected by quantum effects
Cosmic and electromagnetic radiation can cause errors

14. Errors and faults
Fault, error and failure are often used synonymously in the literature, but they are related by the following cause-and-effect relationship:
faults are the cause of errors
errors are the cause of failures

15. Faults Faults happen at the physical level
There are many kinds of faults
Can be distinguished into permanent (manufacturing faults or damage) and transient (faults due to radiation or quantum effects)

16. Errors Similarly errors can be classified as:
Hard errors (due to permanent faults)
Soft errors (due to transient faults)
Can be modeled simply as bits having an incorrect value permanently or temporarily
A reliable design should be able to recover from soft errors

17. Design for Reliability
Triple Modular Redundancy (TMR)
Error detecting and/or correcting codes
Parity
Hamming codes
Block codes
Cyclic Redundancy Check (CRC)

18. TMR
Simply triplicate the module that must be designed reliably, use majority voter to determine correct output
Assumes errors can occur to only one module at a time

19. Hamming distance
Hamming distance between two n-bit vectors is the number of bits in which they differ.
Example: The Hamming distance between “1010” and “0011” is 2

20. Error detecting codes
In order to detect errors we need to add error detection bits to the data
Error detecting codes are based on the idea that the data together with the error detection bits form a code, which has legal and illegal codewords.
An error should change a legal codeword into an illegal one.

21. Parity bit
The Parity bit is based on adding a single bit to the data so that the total number of ‘1’ is either odd or even
Data bits Even parity code Odd parity code

22. Error-correcting and multiple error-detecting codes
By inserting more than one bit according to some rules, multiple errors can be detected or even corrected
Hamming codes
Bits in positions that are a power of 2 are even parity check bits
Check bits are associated with the information bits which have a 1 in the same bit in binary (starting from bit 1):
Check bit 1: information bit 1, 3, 5, 7 (001, 011, 101, 111)
Check bit 2: information bits 2, 3, 6 and 7 (010, 011, 110, 111)
Check bit 3: information bits 4, 5, 6, 7 (100, 101, 110, 111)
Example:
Information bits 0000 becomes
Information bits 0101 becomes
Single error correction example:
Instead of we receive
Check bit 1 yields error, check bit 2 yields correct, check bit 3 yields error.
The common information bits in check bit 1 and check bit 3 are 5 and 7, but there is no error in bit 7 (check bit 2), so the error is in bit 5
Double error detection example:
Instead of we receive
Check bit 1 correct, check bit 2 error, check bit 3 correct: The error cannot be corrected