ECE-C690 Final Exam: Dependable Computing - Error Detection and Correction, Exams of Computer Science

Download ECE-C690 Final Exam: Dependable Computing - Error Detection and Correction and more Exams Computer Science in PDF only on Docsity! ECE-C690: Dependable Computing Final Exam March 13, 2009 The midterm is due in class Monday, March 16, 2009. Please answer all questions. You are not allowed to collaborate with others. 1. Answer the following questions. (a) (10 points) A simple technique for error correction is to pick the nearest code word as the correct word once an error has been detected. Develop a hardware design that performs the error correction for a separable 3-of-6 code by choosing the nearest valid code word. Make the necessary assumptions and state them clearly in your answer. Points will be awarded, in part, based on the efficiency of your design. (b) (15 points) The following is a parity matrix for a Hamming code:   d1 c1 d2 c2 d3 c3 d4 0 1 1 1 0 1 0 1 0 0 1 0 1 1 1 1 0 0 1 1 0   where ci is a check bit and di is a data bit. • Write the parity equations for the three check bits. • Using these parity equations, encode the data word: d1d2d3d4 = 0110. • The encoded word 1100001(d1c1d2c2d3c3d4) has a single bit error. Which bit is in error? (c) (10 points) Consider an n-bit code word and show that if the generating polynomial G(X) of a cyclic code has more than one term, all single-bit errors will be detected. 1 2. Answer the following questions. (a) (15 points) Investigate the error detection capability of the following time redundancy approach when used on a ripple-carry adder. During the first addition, the operands are encoded using a 3N arithmetic code. During the second addition, the operands are encoded using a 5N arithmetic code. Will this scheme detect any single error that can occur in the adder, and why? Will this approach detect any double errors that can occur in the adder, and why? (b) (10 points) Demonstrate the use of checksums in matrix multiplication to detect, locate, and correct an error by multiplying the following two matrices. You must first augment each matrix to include the necessary checksum rows and columns. Show the augmented matrices, the resulting matrix product, and explain how the erroneous value is located and corrected. Assume that element (2, 2) of the matrix product is calculated incorrectly when demonstrating the technique. A =   3 2 1 2 1 3 6 1 4 5 2 3 7 8 1 0   B =   1 6 3 2 5 2 1 2 2 4 3 1 3 5 2 7   2