Describe practical applications where Binary Coded Decimal (BCD) and Hexadecimal are used
1.1 Data Representation – Practical Applications of BCD & Hexadecimal
Binary Coded Decimal (BCD) 🕰️
BCD is a way of storing each decimal digit (0–9) in its own 4‑bit binary chunk. Think of it like a phone keypad: each key represents a single number, not a combination of numbers. This makes it easy for devices that need to display or process decimal numbers exactly as humans see them.
| Decimal | 4‑bit BCD |
|---|---|
| 0 | 0000 |
| 1 | 0001 |
| 2 | 0010 |
| 3 | 0011 |
| 4 | 0100 |
| 5 | 0101 |
| 6 | 0110 |
| 7 | 0111 |
| 8 | 1000 |
| 9 | 1001 |
Example: The decimal number 45 is stored as 0100 0101 in BCD.
Each digit (4 and 5) is represented separately, so the calculator can display “45” exactly as written.
Hexadecimal (Base‑16) 🛠️
Hexadecimal uses 16 symbols (0–9 and A–F) to represent numbers. It’s like a 16‑level colour palette: each level is a power of 16, making it easier to read long binary values. Computers often use hex because it’s compact and aligns nicely with 4‑bit groups.
| Decimal | Hex | 4‑bit Binary |
|---|---|---|
| 0 | 0 | 0000 |
| 10 | A | 1010 |
| 15 | F | 1111 |
| 16 | 10 | 0001 0000 |
| 255 | FF | 1111 1111 |
Example: The decimal number 255 is written as 0xFF in hex.
Each pair of hex digits represents one byte (8 bits), which is handy when reading memory addresses or writing assembly code.
Real‑World Uses 📊
- BCD: Digital clocks, calculators, and financial software that must display exact decimal values.
- Hex: Memory addresses in debugging, colour codes in web design (e.g.,
#FF5733), and low‑level programming such as assembly language.
Revision
Log in to practice.