CSE-45593 ---------------- HW #1 ------------------ Name: ____________________

Problem 1 (25 Points)

- Three fundamental terms used in this course are
*fault, error,*and,*failure.*In one to three sentences, clearly distinguish these terms from each other. - What is the difference between a
*permanent fault,*an*intermittent fault*, and a*transient fault*in term of fault duration? - Comment on the following statement with justification. Single faults can cause multiple bit errors and multiple faults can cause single error.
- Comment on the following statement with justification. A fault-tolerant system necessarily has a high reliability.
- Define the following:
*reliability, availability, safety*, and*performability*. Does a system with a high availability necessarily have a high reliability?

Problem 2 (15 Points)

Design a one bit 5MR voter.

Problem 3 (15 Points)

A certain cyclic code has the generator polynomial G(x) = x^{5} + x^{2 }+ 1.

- Generate a codeword for the input data 10101.
- Using logic gates, design an appropriate encoder and decoder the given cyclic code.
- Determine the code distance and comment on its error detection capability.

Problem 4 (20 Points)

A 2M X 16 memory system is design using 1 M X 4 chips. Assume chip failure modes are single-bit cell (50%), single-row all-0's (20%), single-column all-0's (20%), and whole-chip all-0's (10%). Also, assume 0 and 1 values are equally likely. Compare and comment on relative performance (single-error-detection coverage) and overhead of the following approaches.

- Bit per chip
- Bit per multiple chips
- Duplication
- Single precision checksum (one sum for the entire memory).

Problem 5 (15 Points)

Design the self dual of a full adder.

Due: Thursday, October 11, 2001