The Hexadecimal numeral system, or "hex," is a base-16 system utilizing sixteen distinct symbols: digits 0 through 9 and letters A through F (representing values 10 through 15). It is the standard format in computing and digital electronics for streamlining binary data representation. Because one hexadecimal digit corresponds exactly to four binary digits (bits), or a "nibble," it provides a compact and efficient method for visualizing complex data.
For example, the binary sequence 1011 (decimal 11) is represented by the single hexadecimal digit B. TA full 8-bit byte, such as 11000101, is condensed into just two digits: (C5). This concise format significantly reduces errors when reading, writing, or debugging code compared to long binary strings.
In instrument control and programming, hexadecimal is essential for handling memory addresses, error codes, and status registers. For instance, a power supply may return a status byte of 0x81 (where 0x denotes hex). An engineer can quickly interpret this as binary 10000001 to verify specific bit flags, such as an active error state or output status.
See the table 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 |