Understand how hexadecimal can be used to represent whole numbers.

The idea

Hexadecimal is base 16, using digits 0 to 9 and letters A to F for the values 10 to 15. Each hex digit maps to exactly four binary bits, so hex is a compact shorthand for whole numbers: the byte 11111111 is FF, and 10100000 is A0. To convert a whole number to hex, either group the binary into nibbles of four bits from the right and translate each, or divide repeatedly by 16 and read the remainders. For example, 200 divided by 16 gives 12 remainder 8, so the hex is C8. To convert back, multiply each digit by its place value (16, 1) and add: C8 is 12 × 16 + 8 = 200. Hex represents whole numbers only here, and is used because it is shorter and less error-prone to read than long binary strings.

What earns the marks

• States that hexadecimal is base 16 with digits 0 to 9 and A to F representing 10 to 15.
• Explains that each hex digit corresponds to four binary bits, so hex is a compact representation of whole numbers.
• Converts a whole number to hex by grouping binary into nibbles or by repeated division by 16.
• Converts hex back to decimal by multiplying each digit by its place value and summing.
• Gives a reason hex is used, such as shorter, more readable strings than binary.

Common mistakes and how to put them right

• Treating A to F as ordinary letters with no numeric value.

  Put it right: Remember A is 10 through to F as 15.

• Grouping binary into nibbles from the left rather than the right.

  Put it right: Group from the rightmost bit so place values align.

• Forgetting that hex place values are powers of 16, not 10.

  Put it right: Multiply the left digit by 16 and add the right digit for a two-digit value.

Exam tips

• Learn the 0 to 15 to hex digit table so conversion is instant rather than counted on fingers.
• When converting binary to hex, pad the leftmost nibble with zeros if needed so every group has four bits.
• Check a hex answer by converting back to decimal and comparing with the original whole number.