The Hexadecimal numeral system, or "hex," is a base-16 system. It uses sixteen distinct symbols to represent values: the digits 0 through 9, and the letters A through F to represent the values 10 through 15. The hexadecimal system is widely used in computing and digital electronics as a more human-friendly way to represent binary data. The primary reason for this is the direct and simple relationship between hexadecimal and binary: one hexadecimal digit corresponds exactly to a group of four binary digits (bits), also known as a nibble.
For example, the binary sequence 1011 is equal to decimal 11, which is represented by the single hexadecimal digit B. This makes converting between binary and hexadecimal very straightforward. A full byte (8 bits), like 11000101, can be represented by just two hexadecimal digits (C5), which is much more compact and less error-prone to read and write than the long binary string.
In the context of programming and debugging instrument control, hexadecimal is often used to represent memory addresses, error codes, status registers, or raw data packets. For example, a status byte read from a power supply might be 0x81 (the 0x prefix indicates a hex number), which the programmer can then quickly interpret as the binary value 10000001 to check the state of individual status bits.
See the graph for conversion to binary and decimal numbers.
| Binary numbers | Hexadecimal | Decimal |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 10 | 2 | 2 |
| 11 | 3 | 3 |
| 100 | 4 | 4 |
| 101 | 5 | 5 |
| 110 | 6 | 6 |
| 111 | 7 | 7 |
| 1000 | 8 | 8 |
| 1001 | 9 | 9 |
| 1010 | A | 10 |
| 1011 | B | 11 |
| 1100 | C | 12 |
| 1101 | D | 13 |
| 1110 | E | 14 |
| 1111 | F | 15 |