(1). Using the ASCII-Binary Character Table (which is attached in the last page), convert the following data in to binary: COSC (2). The binary pattern for the above data is a string of 32 bits. Divide the data string to 8 message blocks. Each of the blocks consists of 4 bits. (3). Encode each of the 8 blocks into a codeword of 7 bits, using the Encoding rules presented in the previous pages. (4). By Step (3) above, you get 8 codewords. You randomly pick up 4 codewords. For each of the 4 codewords, you intentionally change ONE bit to make an error. Then, using the Error-Correcting and Decoding Procedures presented in the previous pages, correct the error for each of the 4 words. (Please write your detailed procedures on your worksheet.) ASCII - Binary Character Table Letter ASCII Code a 097 098 099 100 101 102 103 h 104 105 106 k 107 108 m 109 n 110 111 P 112 113 114 S 115 t 116 u 117 V 118 w 119 ? 120 ? 121 Z 122 OUOO - Eco- Binary 01100001 01100010 01100011 01100100 01100101 01100110 01100111 01101000 01101001 01101010 01101011 01101100 01101101 01101110 01101111 01110000 01110001 01110010 01110011 01110100 01110101 01110110 01110111 01111000 01111001 01111010 Letter ASCII Code Binary A 065 01000001 B 066 01000010 ? 067 01000011 D 068 01000100 E 069 01000101 F 070 01000110 G 071 01000111 H 072 01001000 1 073 01001001 ] 074 01001010 K 075 01001011 L 076 01001100 M 077 01001101 N 078 01001110 079 01001111 P 080 01010000 081 01010001 R 082 01010010 S 083 01010011 T 084 01010100 U 085 01010101 V 086 01010110 w 087 01010111 ? 088 01011000 Y 089 01011001 Z 090 01011010 2000OZ3 - I Encoding: Given a piece of data, for example, ", before it is stored in a storage system (such as the memory system of a computer or a CD), it is first converted into binary string. Using the ASCII, Hi is converted to: 01001000 01101001 To use the Hamming code, the data (in binary) is divided into blocks; each block consists of 4 bits. The block of data bits is denoted by (ml, m2, m3, m4). We call these bits, namely, ml, m2, m3, and m4, message bits. Then, each data block of 4 bits is encoded to a codeword of length 7 (that is, 7 bits), denoted by (ml, m2, m3, m4, rl, r2, r3) with three check bits, namely, r1, r2, and r3, being appended to the message block of 4 bits, forming a codeword of 7 bits (as showed above). The check bits are determined by the following equations: rl - ml + m2 + m4 (which is called Parity check A) r2 = ml + m3 + m4 (which is called Parity check B) 13 m2 + m3 + m4 (which is called Parity check C) In these parity checks, + is the Exclusive OR operation, that is, 0+ 0-0, 0+1+1, 1+0=1, and 1 +1 -0 Please note that the Exclusive OR operation for 3 bits is done as follows: 1+1+1 = (1+1)+1 - 0+1=1, and 0+1+1=(0+1+1+0+1=1, for example, Then, in the memory systems, the codewords (consisting of both message bits and check bits), rather than only the message bits, are stored. Error correction and decoding: When accessing data from the storage system, suppose a 7-bit word is read from the storage, say, (ml, m2, m3, m4, r1, r2, r3). It may contain some error. The procedures for error detection and correction are as follows: There is no error if and only if All 3 parity checks, A, B, C, are satisfied ml is wrong if and only if Parity checks A and B are not satisfied (as ml appears in A and B, but not in C) m2 is wrong if and only if Parity checks A and Care not satisfied m3 is wrong if and only if Parity checks B and C are not satisfied m4 is wrong if and only if Parity checks A, B and C are not satisfied rl is wrong if and only if Parity check A is not satisfied r2 is wrong if and only if Parity check B is not satisfied if and only if Parity check C is not satisfied r3 is wrong
