Digital logic designing presentation
- 1. ERROR DETECTION & CORRECTION CODES Presented by: Faraz Ahmad Muhammad Qasim Faiz Ul Hassan 1
- 2. ERROR DETECTION AND CORRECTION CODES When the digital information in the binary form is transmitted from one circuit or system to another circuit or system an error mayoccur. This means the signal corresponding to 0 may change to 1 or vice-versa due to presence of noise To maintain data integrity between transmitter and receiver, extra bit or more than one bit are added in the data. These extra bits allow the detection and sometimes the correction of error in the data. 2
- 3. TYPES OF ERROR: There are two types of errors. Single bit error. Burst error. Single bit error: There is only one bit changed in the code. 10101 10100 Burst error: There are more than one bit changed in received code. 101010010 111010011 Here the length of error is six after six bits error is occuring. Changed bit Changed bits
- 4. DETECTION AND CORRECTION OF ERROR Codes which allow only error detection are called error detecting codes and codes which allow error detection and correction are called error detecting and correcting codes Types of error detector. Simple parity bit(even, odd) 2d parity Check sum CRC(cyclic redundancy check)
- 5. Parity bit • A parity bit is used for the purpose of detecting errors during transmission of binary information. • A parity bit is an extra bit included with a binary message to make the number of 1s either odd or ERROR DETECTION: 3
- 6. The parity error detection system just described detects any odd number of errors. However, it cannot detect an even number of error because such errors will not destroy the parity of the transmitted group ofbits Block parity: When several binary words are transmitted or received in succession, the resulting collection of bits can be regarded as a block of data, having rows and columns. Example: four eight bit words in succession form an 4x8block. Parity bits can then be assigned to both rows andcolumns. This scheme is known as block parity It makes it possible to correct any single error occurring in a data word and to detect any two errors in aword. CONTD… 6
- 7. CORRECTION OF ERRORS Correction of error is doned by using hamming code method. This method is used for both the detection and for the correction of error code send to the reciever
- 8. HAMMING CODE Hamming code not only provides the detection of a bit error, but also identifies which bit is in error so that it can be corrected. Thus hamming code is called error detecting and correcting code. The code uses a number of parity bits(dependent on the number of information bits) located at certain position in a group. Number of parity bits: The number of parity bits depends on the number of information bits If the number of bits is designated as x, then the number of parity bits P is determined using the relation 2𝑝 ≥ 𝑥+ 𝑃+1
- 9. CONTD… Location of the parity bits in a code: • The parity bits are located in the positions that are numbered corresponding to ascending powers of two(1,2,4,8,….). • Therefore, for 7-bit code, locations for parity bits and information bits are as follows: D4, D3,D2,P3, D1,P2,P1 Assigning values to parity bit: • In hamming code , each parity bit provides a check on certain other bits in the total code, therefore we must know the value of these others in order to assign the parity bit value.
- 10. CONTD… Assignment of P1: This parity bit checks all bit locations, including itself, that have 1s in the same location in the binary location numbers. Assignment of P2: This parity bit checks all bit locations, including itself, that have 1s in the middle bit. Assignment of P3: This parity bit checks all bit locations, including itself, that have 1s in the left-most bit.
- 11. SINGLE ERROR CORRECTION AND DOUBLE ERROR DETECTION With the light modification, it is possible to construct hamming code for single error correction and double error detection. A one more parity bit is added in the hamming code to ensure hamming code contains an even number of ones. The resulting hamming code enables single error correction and double error detection. When overall parity bit is correct, there is no single error during the transmission of the code. If overall parity bit is incorrect, then there is single error and the bit position of the error can be indicated by binary number formed after checking the parity bits.