5. Suppose we want an error-correcting code that will allow all single-bit errors to be corrected for memory words of length 10. a. How many parity bits are necessary? b. Assuming we are using the Hamming algorithm presented in this chapter to design our error-correcting code and an odd parity, find the code word to present the 10-bit information word: C. 1 0 0 1 1 0 0 1 1 1 We now receive the following code word: 1 0 1 0 1 1 0 0 0 0 1 0 1 1 Is this a legal code word, assuming an odd parity? If not, what is the corrected code word? (Which bit is the error bit?)

5. Suppose we want an error-correcting code that will allow all single-bit errors to be corrected for memory words of length 10. a. How many parity bits are necessary? b. Assuming we are using the Hamming algorithm presented in this chapter to design our error-correcting code and an odd parity, find the code word to present the 10-bit information word: C. 1 0 0 1 1 0 0 1 1 1 We now receive the following code word: 1 0 1 0 1 1 0 0 0 0 1 0 1 1 Is this a legal code word, assuming an odd parity? If not, what is the corrected code word? (Which bit is the error bit?)

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Design an BCH(10,6) which utilises unusable numbers. Assume that we can either drop the double error correction requirement for those unusable numbers, or make the code length longer. You must explain how the coding method of design an BCH(10,6) works, why it works, and what both the gains and the drawbacks are.
Using the SEC-DED Hamming code given in class (for 4 bit words), determine whether there is no error, an error in one bit, or an error in two bits for the following 8 bit word fetched from memory. If there is an error in one bit, indicate which bit is in error. 0011 1011
5. Suppose we want an error-correcting code that will allow all single-bit errors to be corrected for memory words of length 10. a. How many parity bits are necessary? b. Assuming we are using the Hamming algorithm presented in this chapter to design our error-correcting code and an odd parity, find the code word to present the 10-bit information word: 1 0 0 1 1 0 0 1 1 1
Using the Hamming code given in class for 8 bit data words, determine whether there is an error, and if so, in which bit, for each of the following words fetched from memory: 0010 0011 0010
Scenario: In a biased N-bit binary number system with bias B, positive and negative numbers are represented as their value plus the bias B. For example, for 5-bit numbers with a bias of 15, the number 0 is represented as 01111, 1 as 10000, and so forth. Biased number systems are sometimes used in floating point mathematics. Consider a biased 8-bit binary number system with a bias of 12710 Question: What is the representation and value of the most negative number?
5. Consider the binary numbers s= (0.101)2, r= (10.101) 2. (a) For fl(r) the floating point value using the Rounding to Nearest rule, write out bits 47-52 of the mantissa. (b) Converts and a to base 10 (without rounding). Your answers should be expressed as fractions.
The table below represents a line in the code for Hamming's code where d = 12 and m = 5. Compute the syndrome and determine if there is an error and which bit, 1-17, is wrong. Recall that if there is no error then position 0 is given as the "error position." 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 D po P1 d11 P2 d10 d9 dɛ p3 d7 do ds dą dz d2 d1 P4 do ? 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 So = [ Select ] S1 = [ Select ] S2 = [ Select ] S3 = [ Select ] S4 = [ Select ] Error Position = [ Select ]
Question 1. and {C,D} form the two 2-bit numbers N1 and N2. The circuit will perform the difference N1 – N2 and gives output bits F (MSB) and G. Assume that the circuit never sees the combinations of inputs in which N1 is less than N2 i.e. you can regard those input combinations as don't care Consider a 2-bit binary subtractor defined as follows. The inputs {A,B} conditions. а. Fill in the truth table for F and G. b. Fill in the K-map for the minimum sum of products expressions for the function F and G.
Consider a code with only four valid codewords: 0000000000,0000011111,11111100000,11111111111. a)what is the hamming distance in this given code? b)prove your answer (a)? c)what is the lower limit on the check bits for this code to correct single errors?
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2. Add-4.63mx 10 to -5.96us x 10', assuming that you have only three significant digits, first with guard and round digits and then without them.