Denary to Hexadecimal using Binary

Going through binary is a reliable way to turn a denary number into hexadecimal, because a byte splits neatly into two halves and each half is exactly one hex digit. It also gives you a way to check an answer you found by dividing by 16.

Write the number as 8 bits

First convert the denary number into 8-bit binary using the place values 128, 64, 32, 16, 8, 4, 2 and 1. Take each place value that fits into what is left over, then pad with leading zeros until there are exactly eight bits.

For 197: 128 fits, leaving 69. The 64 fits too, leaving 5. The 32, 16 and 8 do not fit, but the 4 does, leaving 1, and then the 1 fits. The unused places hold 0, giving 11000101.

Split into nibbles and convert each one

Break the eight bits into two nibbles of four bits: 1100 and 0101. Each hex digit represents exactly one nibble, so the left nibble becomes the first hex digit and the right nibble becomes the second. Convert a nibble using its own place values of 8, 4, 2 and 1, and write any total from 10 to 15 as its letter.

Reading the two digits in order gives C5, so 197 is C5 in hexadecimal. You can check it: C is 12, and 12 × 16 + 5 = 197.

A nibble can only ever total 0 to 15, which is why this method can never produce a digit beyond F.

Numbers below 16

A denary number under 16 fits inside four bits, so its left nibble is 0000 and the answer begins with 0. The number 9 is 00001001, which splits into 0000 and 1001: 0 and 9, giving 09 rather than 9. Keeping the zero means the answer is always two hex digits long, matching one byte.