5. Hamming Codes a) Suppose we want an error correcting code that will allow all single-bit errors to be corrected for memory words of length 15. How many check bits are necessary? b) Suppose we are now working with memory words of length 8. We have already calculated that we need 4 check bits, and the length of all codewords will be 12. We now receive the following code word: 010011011111 Is this a legal codeword, assuming even parity? If not, where is the error?

5. Hamming Codes a) Suppose we want an error correcting code that will allow all single-bit errors to be corrected for memory words of length 15. How many check bits are necessary? b) Suppose we are now working with memory words of length 8. We have already calculated that we need 4 check bits, and the length of all codewords will be 12. We now receive the following code word: 010011011111 Is this a legal codeword, assuming even parity? If not, where is the error?

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

See similar textbooks

Similar questions

You are given two bit locations, i and j, together with the 32-bit values N and M. To insert M into N, provide a procedure that starts M at bit j and finishes it at bit i. It is safe to presume that all of M can fit in the bits j through i. In other words, you may infer that there are at least 5 bits between j and i if M = 10011. M could not completely fit between bit 3 and bit 2, thus you would not, for instance, have j = 3 and i = 2.
2 Suppose you are given an alphabet consisting of several symbols as well as the frequencies with which the symbols appear. The Huffman code is an encoding of each symbol as a binary string which among all prefix codes minimises the expected length of an encoded text. Your task is to find the lengths of all these binary strings. - Suppose the alphabet consists of the following symbols with given frequencies. Symbol G Frequency 33 H 37 1 39 J 11 K 10 L 31 M 56 N 22 What is the set of codeword lengths in a Huffman code for this alphabet? Select one alternative: O (2,2,3,3,3,4,5,5} {2,2,3,3,4,4,4,4} {2,3,3,3,3,3,4,4} O {2,2,2,3,4,5,6,6}
Answer the given question with a proper explanation and step-by-step solution. Consider a Hamming (7.4) code in which the parity bits are calculated according to the following equations: r0 = a0 + a1 + a2 r1 = a1 + a2 + a3 r2 = a0 + a1 + a3 The following dataword is to be coded with this scheme: format: a3 a2 a1 a0 0010 What is the parity code for the above dataword? Show it in decimal format for (r2,r1,r0); e.g. if the resulting bits are r2=1, r1=0, r0=0 (100), type the decimal equivalent of 100, which is 4.
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 ]
4, in the fixed-point machine, the following statement is wrong ( ).A. In addition to the complement, the original code and the inverted code cannot indicate that the original code of −1 B. +0 is not equal to −0C. the inverse of +0 is not equal to the negative of −0 D. For the same machine word length, the complement code can represent a negative number more than the original code and the inverted code.
14. For this question, mark all answers that apply. Assuming that i, j, and k are all 32-bit int and a, b, and c are all normal 32-bit float, and that no values go out of range, which of the following must be true? a* (b*c) = (a*b)*c If a>0 and b>0, then (a+b) >a i+(j+k) i*(j*k) (i+j)+k == == == (i+j)+k (i*j)*k k+(j+i)
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?
5. Let the content of register $t1 represent a 2's complement number N. Write a MIPS code fragment such that the register $t2 stores the absolute value of N. In other words, register $t2 has a copy of register $t1 if N is positive, and $t2 should hold the negative of N, if N is negative.
Problem: You have the table below of values of telemetry from the satellite. The temperatures are encoded linearly in unsigned binary bytes as a function of time. The samples come in every five minutes starting at time = 0. The temperatures are in degC and the temperature of -50 degC corresponds to a telemetry value of 0, while a temperature of 100 degC corresponds to a telemetry value of 255. (All values are decimal unless explicitly stated otherwise.) Write down the equation that describes the temperature as a function of telemetry value in the form of T = a* TV + b. What is the value of a? What is the value of b? After your data has been downlinked, as shown in the table below, fill in the Time and Temperature columns (to one place past the decimal point for the Temperature). Sample Telemetry value Time (minutes) Temperature (degC) 1 2 3 4 5 6 7 8 9 10 11 12 13 10 12 14 17 21 41 81 181 210 220 215 222 225 0 5 10 60 -44.1 -42.9 -41.8 82.3
Using the Hamming code given in classfor 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: A.0010 0011 0010 B.0110 0011 1010
Consider a binary code that consists of only four valid code wards as given below: 00000, 01011, 10101, 11110 Let the minimum Hamming distance of the code be p and the maximum number of erroneous bits that can be corrected by the code be q. Then the values of p and q are
Let C be the ternary linear code with basis B = {11012, 21220, 22120} with information bits in positions 2, 3, and 4. State the codeword a that encodes the message m = 202: