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:
d1c1d2c2d3c3d4
0111010
1001011
1100110
where ciis a check bit and diis 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.
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