Numbers: How to convert binary integers to their hexadecimal equivalents and vice versa

Converting between binary and hexadecimal is straightforward because each hex digit maps directly to a 4-bit nibble. This makes hex a convenient shorthand for binary.

Key points

• To convert binary to hex: split the binary number into NIBBLES (groups of 4 bits from the right). Convert each nibble to its hex equivalent.
• To convert hex to binary: convert each hex digit to its 4-bit binary equivalent. Combine the nibbles.
• Example: binary 10110010 = nibbles 1011 and 0010 = hex B2.
• If the binary number does not divide evenly into nibbles, pad with leading zeros on the LEFT.
• Exam Tip:Always split into groups of 4 FROM THE RIGHT. 11010 becomes 0001 1010 (padded), not 1101 0.
• Common Mistake:Dropping the trailing zero in hex. Binary 10110000 = B0, NOT just B. The 0 is significant.
• Exam Tip:Check your answer by converting BACK. If you got hex B for 10110000, convert B back to binary = 1011, which is NOT 10110000. This tells you the answer is wrong (it should be B0).