IPv$4$ addresses, such as $192\mathrm{.}168\mathrm{.}1\mathrm{.}1,$ are typically presented in decimal format for human readability. However, computers and network devices process these addresses in binary form. The ability to convert between decimal and binary, and vice versa, is crucial for understanding network behaviors and effectively designing, implementing, and managing IP networks.

Each octet of an IPv$4$ address, that is$,$ a number between $0$ and $255,$ corresponds with an $8-$bit binary number. Here's the step$-$by$-$step process using positional weights to convert a decimal number to its binary form.

Identify the positional weights: Each bit position in an $8-$bit binary number represents a specific weight. From right to left, these are $2$

$,2$

$,2$

$,2$

$,2$

$,2$

$,2$

$,$ and $2$

$.$

Determine which weights sum up to the specific decimal number: Starting from the highest bit $($leftmost$),$ determine the highest power of $2$ that is less than or equal to the decimal number. This bit gets a $\text{'}1\text{'}.$ Subtract the value of this power from your decimal number.

Repeat for the remaining amount: With the remainder, repeat Step $2$ for the next highest power of $2,$ and continue until the remainder is zero or all bits are accounted for.

Fill in the lower bits: If any bits have not been assigned and still need to be accounted for, they will be $\text{'}0\text{'}.$