# M out of N coding scheme And its efficiency

In this coding scheme we have N total number of bits and fixed M of those bits are 1s and N – M bits are 0s. Hence this scheme is called M out of N coding scheme. It is a type of Error-Detecting coding scheme as if during transmission we have any error in the message we can see that if number of 1s in the message is same. If they are not same then there is an error during transmission. Hence error is detected. 2 out of 5 codes is such an example

Biquinary code (2 out of 7) with weights as 5043210 is such an example.

5           0             4             3              2              1              0           Decimal equivalent

0              1              0              0              0              0            1                  0

0              1              0              0              0              1          0                  1

0              1              0              0              1              0             0                  2

0              1              0              1              0              0              0                  3

0              1              1              0              0              0              0                  4

1              1              0              0              0              0              0                  5

1              0              0              0              0              1              0                  6

1              0              0              0              1              0              0                  7

1              0              0              1              0              0              0                  8

1              0              1              0              0              0              0                  9

Efficiency:           As we can represent only 10 digits using 7 bits while in binary representation we can represent 27 numbers. Hence

Efficiency = (10/ 128)*100 = 8% (approx.)