Digital Electronics NUMBER SYSTEM BINARY CODES TYPES OF BINARY CODES BCD CODE EFFICIENCY OF BCD EXCESS-3 CODE GRAY CODE M out of N CODING SCHEME with EFFICIENCY PARITY BIT ERROR DETECTION by PARITY QUESTION HAMMING CODE (General form) Relation of PARITY BIT with MESSAGE BITS ILLUSTRATION-I ILLUSTRATION-II BOOLEAN ALGEBRA K MAPS COMBINATIONAL CKT SEQUENTIAL CIRCUITS TIMING CIRCUITS

Hamming code:

This code is used for single error correction i.e. using this code we can detect only single error. In parity bit method we used only single extra bit but in this method number of extra bits (which also are parity bits) vary with the number of bits of the message.

Suppose we have the number of information bits as m=4 then we have to determine number of parity bits using above relation

2p >= 4 + p + 1

2p >= 5 + p

From this we can check for values of p, which one satisfies

For p=1                                 2 >= 6 doesn’t satisfy

For p=2                                 4>= 7 doesn’t satisfy

For p=3                                 8>=8 satisfies hence we have p=3

So now we have 4 information bits and 3 parity bits so total of 7 bits. In the parity bit method, we placed the parity bit at rightmost position. But here we don’t place the extra bits consecutively but the positions are fixed by following rule:

As we need only three positions so we have to pick first 3 which are 1, 2, and 4.

So we have the composition of hamming code as follow:

Bit1        bit2       bit3        bit4        bit5        bit6        bit7

Parity    parity                    parity

P1                  P2                  M1               P3                  M2               M3               M4

Now we have to decide positions in the hamming code which would be covered by the parity bit i.e. the positions considering which value of parity bit would be decided. We’ll be using following rule for this: