How to Convert from Hexadecimal to Binary?
To cross-validate the conversion, we’ll reuse the same example from our binary-to-hexadecimal demonstration. By reversing the process—converting the hexadecimal result back into binary—we can check whether it matches the original binary number \(\mathsf{1011.00111}\). This way, we ensure the accuracy of our method and reinforce the understanding of both forward and reverse conversions.
Example: Let’s convert \(\mathsf{7B.34_{16}}\) to Binary (Base-2).
To convert a hexadecimal number that contains a fractional part into its binary equivalent, start by locating the radix point—the key marker that separates the whole number portion from the fractional component. From this point, work outward in both directions: move left to process the digits of the whole part and move right to handle the digits in the fractional part. For each hexadecimal digit you encounter, actively replace it with its corresponding 4-bit binary representation, making sure to include leading zeros if necessary so that each group maintains a consistent width of four bits.
As you continue this process, double-check that all bits are properly aligned relative to the binary point to avoid any misplacement or confusion. After completing the conversion of each digit and ensuring the integrity of every binary segment, combine all the binary groups—both from the whole side and the fractional side. This final arrangement gives you the accurate binary representation of the original hexadecimal number, with no loss of precision.
Before starting the conversion, consult the reference chart showing the binary equivalent of each hexadecimal digit. This chart helps reinforce understanding and speeds up the process. It’s a good idea to memorize the chart early on, as it makes conversions quicker and more intuitive. With regular practice, switching between hexadecimal and binary becomes second nature—an essential skill in digital system design and analysis.
The actual conversion for this example is shown here
Did we Get it Right?
Exactly—when the binary equivalent aligns perfectly with the hexadecimal original, it shows just how precise this method is. Grouping binary digits into sets of four and substituting with their hex counterparts ensures the conversion holds the true value without any rounding or approximation. This kind of integrity in representation is crucial in digital systems, where accuracy and predictability go hand in hand.