any idea how to make this circuit or just give me the truth table.....i really don't know how to start the truth table


please give me an idea...thanks

 

Hello Jenny, not sure where you are starting from so ask for more if needed.

If H is a Hamming correction matrix (table) -
and z is the code (vector) sent then

If H times z transposed = the zero vector (all zeros) z is correct.
If not then the decimal value of z gives us the position of the bit that is in error.

When we do matrix multipication the rule is 'rows into columns'
So we multiply corresponding elements of the first row in H by corresponding elements in z and add them all up, to obtain the first entry in the result vector, which is also a column vector.

To do this we use the 4 rules

0x0=0
0x1=0
1x0=0
1x1=1

For each individual multiplication. Please note these rules have the same truth table as an exclusive-or gate giving us a clue how to perform the calculation electronically.

The addition is performed by the following 4 rules

1+1=0
1+0=1
0+1=1
0+0=0

The length of the z vector is the number of bits. It is also equal to the number of columns in the H matrix.
For true Hamming codes this is an odd number 1, 3, 7, 15 etc and equal to
2^r -1 where r is the number of rows in the H matrix.


1010101
0110011
0001111

The 7 bit code is often extended with a parity bit to 8 bits.
The H matrix for this scheme is

1010101
0110011
0001111
1111111