Digital Electronics: Principles, Devices and Applications

Binary Codes 456. What is a parity bit? Define even and odd parity. What is the limitation of the parity code when itcomes to detection and correction of bit errors?7. What is the Hamming distance? What is the role of the Hamming distance in deciding the errordetection and correction capability of a code meant for the purpose? How does it influence theinformation throughput rate?8. With the help of the generalized form of the Hamming code, explain how the number of parity bitsrequired to transmit a given number of data bits is decided upon.Problems1. Write the excess-3 equivalent codes of (6) 10 , (78) 10 and (357) 10 , all in 16-bit format.0011001100111001, 0011001110101011, 00110110100010102. Determine the Gray code equivalent of (10011) 2 and the binary equivalent of the Gray code number110011.11010, (100010) 23. A 16-bit data word given by 1001100001110110 is to be transmitted by using a fourfold repetitioncode. If the data word is broken into four blocks of four bits each, then write the transmitted bitstream.10011001100110011000100010001000011101110111011101100110011001104. Write (a) the Hamming (7, 4) code for 0000 using even parity and (b) the Hamming (11, 7) codefor 1111111 using odd parity.(a) 0000000; (b) 001011101115. Write the last four of the 16 possible numbers in the two-bit quaternary Gray code with 0, 1, 2 and3 as its independent digits, beginning with the thirteenth number.33, 32, 31, 30Further Reading1. Tokheim, R. L. (1994) Schaum’s Outline Series of Digital Principles, McGraw-Hill Book Companies Inc., USA.2. Gillam, R. (2002) Unicode Demystified: A Practical Programmer’s Guide to the Encoding Standard, 1st edition,Addison-Wesley Professional, Boston, MA, USA.3. MacWilliams, F. J. and Sloane, N. J. A. (2006) The Theory of Error-Correcting Codes, North-HollandMathematical Library, Elsevier Ltd, Oxford, UK.4. Huffman, W. C. and Pless, V. (2003) Fundamentals of Error-Correcting Codes, Cambridge University Press,Cambridge, UK.