Error Detection in Binary Codes - Parity Check Bit

Question

This seems like a super easy question but can't get my head around it.

So I have 5 bit-binary as:

A = 00001 B = 00010 C = 00011

When adding the parity check bit it becomes,

A = 000000 B = 000011

I thought when adding the parity check bit the aim was to make it so that it is a even number of 1's, so wouldn't it make sense to add a 1 to the A? Then add 1 to the B?

Answer 1

$B$ becomes $000101$ after adding a parity bit.

$C$ becomes $000110$ after adding a parity bit.

$A$ becomes $000011$ after adding a parity bit.

Your second $A$ makes no sense, as it is not a lengthening of your first $A$, and likewise for $B$.

If the original vector had an odd number of $1$'s, add a $1$. Otherwise add a $0$.