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
- Convert the denary number to an 8-bit binary value.
- Split the binary value into two nibbles (groups of 4 bits).
- Convert each nibble to its denary value (0 to 15).
- Write each value as a hex digit using the A to F table for 10 to 15.
Example — Convert denary 28 to hex.
- Binary 28 in 8 bits is 0001 1100.
- Split into nibbles: 0001 and 1100.
- 0001 = 1, so the first hex digit is 1.
- 1100 = 12, so the second hex digit is C.
- Denary 28 = hex 1C.
Denary to hex, Method 2: divide by 16
- Divide the denary number by 16. The whole part is the first hex digit; the remainder is the second hex digit.
- Convert any value 10 to 15 to its hex letter (A to F).
Example — Convert denary 163 to hex.
- 163 ÷ 16 = 10 remainder 3.
- First digit = 10 = A. Second digit = 3.
- Denary 163 = hex A3.
Hex to denary, Method 1: via binary
- Convert each hex digit to a 4-bit binary nibble.
- Join the two nibbles into an 8-bit binary number.
- Convert the binary number to denary using place values.
Example — Convert hex B9 to denary.
- B = 11, so the first nibble is 1011.
- 9 = 9, so the second nibble is 1001.
- Combined: 1011 1001.
- Place values: 128 + 32 + 16 + 8 + 1 = 185.
Hex to denary, Method 2: multiply by 16
- Multiply the first hex digit by 16.
- Add the second hex digit to the result.
Example — Convert hex 79 to denary.
- 7 × 16 = 112.
- 112 + 9 = 121.
Paper 1 is sat without a calculator. If mental multiplication by 16 feels risky, just use method 1 (via binary) for both directions. Either route is awarded full marks.