Solution

For $7$ bit Hamming code, parity positions are

$1,2,4$

Data positions are

$3,5,6,7$

Given data bits are

$1101$

So,

$D_1=1,\ D_2=1,\ D_3=0,\ D_4=1$

Arrange them as:

$P_1\ P_2\ D_1\ P_4\ D_2\ D_3\ D_4$

$=P_1\ P_2\ 1\ P_4\ 1\ 0\ 1$

For even parity,

$P_1$ checks positions $1,3,5,7$

$P_1+1+1+1=\text{even}$

$P_1=1$

$P_2$ checks positions $2,3,6,7$

$P_2+1+0+1=\text{even}$

$P_2=0$

$P_4$ checks positions $4,5,6,7$

$P_4+1+0+1=\text{even}$

$P_4=0$

Therefore, Hamming code is

$1010101$

Solution

A self-complementing code is a code in which the $9$'s complement of a decimal digit is obtained by complementing all bits.

$8421$ code is not self-complementing.

$2421$ code is self-complementing.

Excess-$3$ code is also self-complementing.

So, correct codes are:

(b) and (c)

Solution