Number Systems

There are two methods for each direction. Method 1 goes through binary as a stepping stone and is foolproof; method 2 uses arithmetic directly and is faster once you are confident.

Denary to hex, Method 1: via binary

1. Convert the denary number to an 8-bit binary value.
2. Split the binary value into two nibbles (groups of 4 bits).
3. Convert each nibble to its denary value (0 to 15).
4. Write each value as a hex digit using the A to F table for 10 to 15.

Denary to hex, Method 2: divide by 16

1. Divide the denary number by 16. The whole part is the first hex digit; the remainder is the second hex digit.
2. Convert any value 10 to 15 to its hex letter (A to F).

Hex to denary, Method 1: via binary

1. Convert each hex digit to a 4-bit binary nibble.
2. Join the two nibbles into an 8-bit binary number.
3. Convert the binary number to denary using place values.

Hex to denary, Method 2: multiply by 16

1. Multiply the first hex digit by 16.
2. Add the second hex digit to the result.