Consider an (8,4) binary linear block code with minimum distance of 4. • How many valid codewords are there? • What is the code rate? • What is the minimum weight of the code? • If the code is used for error detection only, how many errors can it detect? • If the code is used for error correction, how many errors can it correct?

Limits of Representation Suppose we use a 16-bit Two's Complement representation for integers. what is the largest positive number that we can represent? show the 16-bit representation of the largest positive integer what is the lowest negative number that we can represent? (be clear: -34 is 'lower' than -33) show the 16-bit representation of the lowest negative number

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 0 1 1 0  Assuming odd parity, is this a legal code word? If not, according to our error-correcting code, where is the error?

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 00 1 1 00 1 1 1 We now receive the following code word: C. 10 10 1 1 0 0 0 0 10 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?)