Number bases: hexadecimal (base 16).

The idea

Hexadecimal is a positional number system with base 16, so it needs sixteen digit symbols: 0 to 9 then A to F, where A = 10, B = 11, C = 12, D = 13, E = 14 and F = 15. Place values are powers of 16: from the right, 16⁰ = 1, 16¹ = 16, 16² = 256 and so on. To convert denary 43, take two sixteens (32) leaving 11, which is B, giving 2B. To convert back, multiply each digit by its place value and add: 2 × 16 + 11 = 43. Hexadecimal is compact because one hex digit represents exactly four binary bits, so a byte is written as two hex digits.

What earns the marks

• States that hexadecimal is base 16 and uses the digits 0–9 plus A–F.
• Recalls that A = 10, B = 11, C = 12, D = 13, E = 14 and F = 15.
• Explains that place values are powers of 16 (1, 16, 256...).
• Converts a denary number to hexadecimal by dividing by 16 and recording remainders, using letters for values 10–15.
• Converts hexadecimal to denary by multiplying each digit by its place value and adding the results.
• Explains that one hexadecimal digit represents four binary bits, so two hex digits represent one byte.

Common mistakes and how to put them right

• Treating A–F as invalid digits.

  Put it right by stating they stand for the values 10 to 15.

• Using base 10 place values when converting.

  Put it right by using powers of 16 (1, 16, 256...).

• Forgetting that a remainder of 11 must be written as B.

  Put it right by converting remainders above 9 into letters.

Exam tips

• Write the hex digit values (A = 10 ... F = 15) at the top of your working before converting.
• Check a conversion by multiplying back out and confirming you recover the denary value.
• Remember two hex digits equal one byte, which helps in multiple-choice questions about representation.