Students must be able to represent decimal values between 0 and 255 in…

The idea

Hexadecimal is base 16, using digits 0–9 and letters A–F for the values 10–15. Any decimal value from 0 to 255 fits in two hexadecimal digits, because 16² = 256, so the largest two-digit value FF equals 15 × 16 + 15 = 255. To convert, split the decimal number into a multiple of 16 plus a remainder: divide by 16, the quotient is the first hex digit and the remainder is the second. For example, 200 ÷ 16 = 12 remainder 8, so 200 = C8 in hexadecimal. Check by reversing: C8 = 12 × 16 + 8 = 200. Values below 16 use a leading zero, so 5 becomes 05. This two-digit representation is why hexadecimal is used for bytes and colour codes.

What earns the marks

• Hexadecimal is base 16 and uses digits 0–9 plus A–F for values 10–15.
• A decimal value from 0 to 255 converts to exactly two hexadecimal digits because 16² = 256.
• Method: divide the decimal value by 16; the quotient gives the first hex digit and the remainder gives the second.
• Worked example: 200 ÷ 16 = 12 remainder 8, giving C8, and C8 = 12 × 16 + 8 = 200 confirms it.
• Values below 16 are written with a leading zero, for example 5 becomes 05.
• FF equals 15 × 16 + 15 = 255, the largest value in the range.

Common mistakes and how to put them right

• Writing the decimal digits unchanged, for example giving 200 as '200' in hex.

  Put it right: Divide by 16 and convert each part to a hex digit, giving C8.

• Using letters beyond F or treating A as 1.

  Put it right: A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.

• Forgetting the leading zero for small values.

  Put it right: Write 5 as 05 so the byte is two digits.

• Reversing quotient and remainder.

  Put it right: The quotient is the first (sixteens) digit and the remainder is the second (units) digit.

Exam tips

• Always show the division by 16 so the method is visible, not just the final answer.
• Check your answer by converting back: multiply the first digit by 16 and add the second.
• Remember the range 0–255 always produces two hex digits, so never write three.
• Learn the letter values A–F as 10–15 so you convert without hesitation.