计算机组织与结构课件全分单元Ch05章节幻灯片.ppt

Hamming code (6) Makes the syndrome word 故障字 Old correct bit c8 c4 c2 c1 New correct bit ⊕c8’ c4’ c2’ c1’ Syndrome word X X X X The syndrome word is error position code “异或” old new Error Correcting Code Function page 149 Hamming code (7) If syndrome contains all 0s , no error , the data is REAL ① If syndrome contains one only one 1 , the old correct bit is error , but the data is REAL ② If syndrome contains more than one 1s, the syndrome value indicates the position of error bit , correct the bit ③ But syndrome value larger than 12, more than one error occurs ④ Error Correcting Code Function page 149 ①② ③ ④ Hamming code (8) E.g. data is 0011 1001 Calculates old check bit: C1(1,2,4,5,7)=1⊕0⊕1⊕1⊕0=1 C2(1,3,4,6,7)=1⊕0⊕1⊕1⊕0=1 C4(2,3,4,8) =0⊕0⊕1⊕0 =1 C8(5,6,7,8) =1⊕1⊕0⊕0 = 0 Stores (m+k) data correct bit: Hamming Code:0011 0 100 1 1 1 1 C8 C4 C2 C1 Hamming code (9) Suppose data bit D3 is changed from 0 to 1 in storage. 0011 0 110 1 1 1 1 ….. When fetches the data , Re-calculates new check bit : C1’(1,2,4,5,7)=1⊕0⊕1⊕1⊕0=1 C2’(1,3,4,6,7)=1⊕1⊕1⊕1⊕0=0 C4’(2,3,4,8) =0⊕1⊕1⊕0 =0 C8’(5,6,7,8) =1⊕1⊕0⊕0 = 0 Hamming code (10) Makes syndrome: c8 c4 c2 c1 0 1 1 1 old ⊕ 0 0 0 1 new 0 1 1 0 syndrome It means position 6 is error, 0011 0 110 1 1 1 1 , corrects the bit 0011 0 100 1 1 1 1 , gets the data bit 0011 1001 出错位取反后就是正确的 Error Correcting Code in semiconductor a Single-Error-Correcting (SEC) code 单纠错码 A double-error-detecting (DED) code 双校验 SEC-DED 单纠错-双校验 For example Hamming code 0011 0110 1111 is just read from main memory, what is real data bits? P152 Answer(1) (1) 2k-1≥m+k —8-bit Data —4-bit check (2) Set up a table 0011 0110 1111 — Data: 0011 1101 — Old check: 0111 Bit Position Position number Check bit