Converting between number bases: hexadecimal: FF

The idea

Hexadecimal is base 16, using digits 0–9 and letters A–F for the values ten to fifteen. To convert FF to denary, expand each place value: the left F sits in the 16¹ place and the right F sits in the 16⁰ place. Each F is worth 15, so the value is 15 × 16 + 15 × 1 = 240 + 15 = 255. To convert FF to binary, replace each hex digit with its 4-bit group: F = 1111, so FF = 11111111. The method generalises: multiply each digit by the appropriate power of 16, working from the right, then add. Always state the base you are converting to and show the place-value expansion so the working can be checked.

What earns the marks

• Recognises that hexadecimal is base 16 and that F represents the denary value 15.
• Expands FF as 15 × 16¹ + 15 × 16⁰, giving 240 + 15.
• States the denary value 255.
• Converts each hex digit to a 4-bit group so FF becomes 11111111 in binary.
• Shows place-value working rather than only a final answer.

Common mistakes and how to put them right

• Treating F as the digit 5 or as an unknown.

  Put it right: F is the hexadecimal digit for fifteen, so it contributes 15 × place value.

• Reading FF as 15 + 15 = 30.

  Put it right: The left digit is multiplied by 16, giving 240, before adding the 15.

• Writing the binary as 1111 only.

  Put it right: Each hex digit becomes its own 4-bit group, so two digits give eight bits: 11111111.

Exam tips

• Write the place values 16¹ and 16⁰ above the digits before multiplying.
• Convert each hex digit to a 4-bit binary group separately to avoid bit-length errors.
• Check the answer by converting back: 255 in denary should return to FF.