How to convert positive denary whole numbers into 2-digit hexadecimal numbers and vice versa

Numbers: How to convert positive denary whole numbers into 2-digit hexadecimal numbers and vice versa

1.2.4a Data Storage: Numbers

Data Storage: Numbers — Note 3 of 5

What you need to know

Hexadecimal (base 16) uses digits 0-9 and letters A-F to represent values 0-15. It is more compact than binary, making it easier for humans to read large binary values. You need to convert between denary and 2-digit hex (00-FF).

What to know

Hexadecimal digits: 0-9 then A=10, B=11, C=12, D=13, E=14, F=15.
Each hex digit represents 4 bits (one nibble).
To convert denary to hex: first convert denary to binary, then convert binary to hex (split into nibbles).
To convert hex to denary: first convert hex to binary, then convert binary to denary.
Two hex digits can represent values 00 (0) to FF (255) — the same range as 8-bit binary.

Key terms

HexadecimalBase 16: A number system that uses sixteen symbols (0-9 and A-F) and is often used as a shorter way of writing binary numbers.

Exam technique

Tip:Hex is used because it is more COMPACT and READABLE than binary — one hex digit replaces four binary digits.
Mistake:Forgetting that hex uses LETTERS after 9. A=10, B=11, C=12, D=13, E=14, F=15.
Tip:To convert 2-digit hex to denary: multiply the FIRST digit by 16, then ADD the second digit. E.g. 2F = (2×16) + 15 = 47.
Mistake:Converting F to binary incorrectly (e.g. 1101 instead of 1111). F = 15 = 1111 in binary.

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