In the world of computing, we often think in terms of binary—the simple language of 1s and 0s. However, reading long strings of binary code is cumbersome and prone to human error. To bridge the gap between machine-level binary and human-readable data, computer scientists use the Hexadecimal system. Often referred to as "Hex," this base-16 numbering system provides a compact and efficient way to represent large binary values.
The Structure of Base-16
Most of us are accustomed to the decimal system (Base-10), which uses ten unique symbols: 0 through 9. In a base-10 system, when we run out of single digits, we move to the "tens" place. Hexadecimal works on the exact same principle of positional notation, but it utilizes sixteen unique symbols instead of ten.
Because we only have ten numerical digits (0–9), we need a way to represent the values ten through fifteen using a single character. To solve this, hexadecimal adopts the first six letters of the alphabet. This allows every single value from 0 to 15 to be represented by one distinct symbol.
| Decimal Value | Hexadecimal Symbol |
|---|---|
| 0–9 | 0–9 |
| 10 | A |
| 11 | B |
| 12 | C |
| 13 | D |
| 14 | E |
| 15 | F |
Exam Tip: Always remember that in hexadecimal, 'A' is not a variable; it is a constant representing the specific value of 10. If you see 'F', immediately think of the number 15.
Understanding Positional Notation
Just like decimal and binary, the value of a digit in hexadecimal depends on its position within the number. In decimal, the positions represent powers of 10 ($10^0, 10^1, 10^2$, etc.). In binary, they represent powers of 2 ($2^0, 2^1, 2^2$, etc.). In hexadecimal, each position represents a power of 16.
Keep reading for free.
Create an account to finish this reading and make it part of your study routine.
Continue reading freeAlready have an account? Log in
Updated