A communications company wants to encode all its data before transmitting anything. We will design a circuit to assist them with this encoding. For the unsigned $3-$bit binary numbers, the encoding requires an extra bit, called $x,$ and can be calculated using even and odd parity. Each number transmitted would have $4$ bits, the $3$ bits of the unsigned binary number and $x.$ The encoding works as follows:

$$ If the number is divisible by $4$ it must be transmitted with odd parity.

$$ All other numbers must be transmitted with even parity.

Again, you can interpret this as the description of a truth table.

Note $0$ is divisible by $4.$ A binary number has odd parity if it contains an odd number of $1$ s$.$ So $111$ and $010$ have odd parity, and $011$ has even parity.

a$.A,B,C,$xxABC