Given are the following codewords for an error control coding scheme data          000             011             100 codeword 00011000   00000111   10101000 . a.What is the minimum Hamming distance? b.  What is the coding rate for this scheme? c. what raw data rate would be required if we need a throughput of 6 Mpbs? d. in a different situation, the number of data bits to transfer is 5, and the minimum hamming distance is dmin=5. find the maximum coding rate for this situation

Suppose we are working with an error-correcting code that will allow all single-bit errors to be corrected for memory words of length 7. We have already calculated that we need 4 check bits, and the length of all code words will be 11. Code words are created according to the Hamming algorithm presented in the text. We now receive the following code word: 1 0 1 0 1 0 1 1 1 1 0 Assuming even parity, is this a legal code word? If not, according to our error-correcting code, where is the error?

The symbol £ is magnified and shown in Figure 1 with a grid superimposed. Figure 1 The image in Figure 1 is to be encoded and encrypted using the following steps: 1. Each of the five horizontal rows of the picture is encoded as a 5-bit binary number. White squares are encoded as Os and black squares as 1s. The horizontal rows are therefore encoded as: Row 1: 00110 Row 2: 01001 Row 3: 11100 Row 4: 01000 Row 5: 11110 2. Starting from the left, the first binary digit is multiplied by 16, the second by 8, the third by 4, the fourth by 2, and the fifth by 1. This will convert the 5-bit binary numbers to decimal numbers as shown below: Row 1: (0 x 16) + (0 × 8) + (1 × 4) + (1 × 2) + (0 × 1) = 0 + 0 +4+2+0 = 6. Row 2: (0 x 16) + (1 × 8) + (0 × 4) + (0 × 2) + (1 × 1) = 0 + 8 +0+0+1 = 9. Row 3: (1 x 16) + (1 × 8) + (1 × 4) + (0 × 2) + (0 × 1) = 16+8+4 + 0 + 0 = 28. Row 4: (0 x 16) + (1 × 8) + (0 × 4) + (0 × 2) + (0 × 1) = 0 + 8 +0+0+0= 8. Row 5: (1 x 16) + (1 × 8) + (1 × 4) + (1 × 2) + (0 × 1)…

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

Consider a hypothetical 8 bit floating point machine representation with a sign bit, a 3 bit exponent, and a 4 bit mantissa (se1e2e3b1b2b3b4), where the exponent bias is 3 (add 3 to exponent of number to form machine representation). Recall that actual mantissa has 5 bits, since the leading 1 is not stored on the machine. (a) What is the number ?≈2.718 in this 8-bit format? (b) What is the number that (10100111)2 represents in this 8-bit format? (c) What is the upper bound of the relative error when representing a real number in this 8-bit format?

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.

Assume that a system uses 10-bit floating-point representation based on the IEEE floating-point format, in which: . There is 1 sign bit. There are k= 6 exponent bits. The exponent bias is 31. . There are n= 3 fraction bits. ● Convert the decimal number -5.5 into the 10-bit IEEE floating point representation explained above. Write the final result in 10-bit binary format. Show your steps.

As the error-detection and correction capability of a code increases, we would expect in general the overhead bits to protect a group of data bits to decrease remain the same increase

Are you able to differentiate between the least significant bit and the most significant bit in a given set of data?

III. Consider the example below that shows both the payload and the two-dimensional parity bits (shown in green), and where exactly one of the payload or parity bits shown has been corrupted. In this example, odd parity is used. - 11000100001111000 01010010010101101 00110111 100011001 11110110011011111 10111011 110011100 00010011 100110000 Please indicate the row and the column location of the bit that has flipped from its original value.