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

E.g.  Consider the parity bit P1 and we have to find the position of message bits which we’ll cover with this parity bit.

Firstly write the binary equivalents of positions of message bit

Bit1        bit2       bit3        bit4        bit5        bit6        bit7

Parity    parity                    parity

P1                  P2             M1                P3           M2               M3               M4

001         010         011         100         101         110         111

Now let’s see in the binary equivalent of position of parity bit P1 that at which position we have 1and we see 1 is at LSB so we select the message bits which have positions with 1 at LSB which are M1, M2 and M4 So P1 bit would check the parity for M1, M2 and M4

E.g.  Consider the parity bit P2 and we have to find the position of message bits which we’ll cover with this parity bit

We have 1 at second position from left so we choose message bits which have 1 at 2nd position n their position’s binary equivalent. Hence we get message bits M1 M3 and M4. So P2 checks parity for message bits of M1 M3 and M4

Similarly we have 1 at 3rd position of P3 message bits with 1 at 3rd position are  M2M3 M4

So we now have

P1 Checks bit number 1,3,5,7

P2 Checks bit number 2,3,6,7

P3 Checks bit number 4,5,6,7

These parity bits can be either even or odd parity bits but all  parity bits must be same i.e. all odd or all even