Uses of Number Systems (Cambridge (CIE) A Level Computer Science) : Revision Note

Applications of Binary Coded Decimal (BCD)

What are the uses of binary-coded decimal (BCD)?

• Binary coded decimal is commonly used in systems that need to display decimal numbers clearly and accurately

• BCD is ideal for applications like digital clocks, calculators, and financial systems where decimal precision matters

• Using BCD avoids rounding errors that can occur in binary-based arithmetic, especially with money and time

• It’s still found in older or embedded systems where simple hardware-based decimal output is needed

Applications of hexadecimal

Why is hexadecimal used?

• In Computer Science hexadecimal is often preferred when working with large values

• It takes fewer digits to represent a given value in hexadecimal than in binary

  • 1 hexadecimal digit corresponds 4 bits and can represent 16 unique values (0-F)

• It is beneficial to use hexadecimal over binary because:

  • The more bits there are in a binary number, the harder it makes for a human to read

  • Numbers with more bits are more prone to errors when being copied

• Examples of where hexadecimal can be seen:

  • MAC addresses

  • Colour codes

  • URLs

MAC addresses

• A typical MAC address consists of 12 hexadecimal digits, equivalent to 48 digits in in binary

  • AA:BB:CC:DD:EE:FF

  • 10101010:10111011:11001100:11011101:11101110:11111111

• Writing down or performing calculations with 48 binary digits makes it very easy to make a mistake

Colour codes

• A typical hexadecimal colour code consists of 6 hexadecimal digits, equivalent to 24 digits in binary

  • #66FF33 (green)

  • 01000010:11111111:00110011

URL's

• A URL can only contain standard characters (a-z and A-Z), numbers (0-9) and some special symbols which is enough for basic web browsing

• If a URL needs to include a character outside of this set, they are converted into a hexadecimal code

• Hexadecimal codes included in a URL are prefixed with a % sign