30 lines
1.8 KiB
Markdown
30 lines
1.8 KiB
Markdown
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---
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obj: concept
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---
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# Hexadecimal System
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The hexadecimal numbering system, often referred to as "hex," is a base-16 numeral system widely used in computing and digital electronics. It provides a convenient way to represent binary-coded values with a more human-friendly and compact notation. In the hexadecimal system, numbers are represented using 16 different digits: 0-9 and A-F, where A stands for 10, B for 11, and so on up to F for 15.
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## Representation
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In hexadecimal, each digit represents a power of 16. The rightmost digit represents $16^0$ (1), the next digit to the left represents $16^1$ (16), the next $16^2$ (256), and so forth. For example:
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- **1F in hexadecimal** is equal to $1×16^1+15×16^0$, which is 31 in decimal.
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- **2A3 in hexadecimal** is equal to $2×16^2+10×16^1+3×16^0,$, which is 675 in decimal.
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## Hexadecimal Digits
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The hexadecimal system uses the following digits:
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- **0, 1, 2, 3, 4, 5, 6, 7, 8, 9**: Represent values 0 to 9.
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- **A, B, C, D, E, F**: Represent values 10 to 15.
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## Uses in Computing
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### Memory Addresses
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In computer programming, memory addresses are often expressed in hexadecimal. Each byte of memory can be represented by two hexadecimal digits, providing a concise way to denote memory locations.
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`Example: 0x1A3F`
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### Color Representation
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Hexadecimal is commonly used to represent colors in web development and digital graphics. In this context, a hexadecimal color code consists of three pairs of digits representing the intensities of red, green, and blue.
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`Example: #FFA500 (RGB: 255, 165, 0)`
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### Binary Representation
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Hexadecimal is closely related to [binary](Binary%20System.md) representation. Each hexadecimal digit corresponds to four bits in binary. This relationship makes it easier to convert between hexadecimal and binary.
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`Example: Binary 1010 is equivalent to Hex A.`
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