| Binary (Base 2) | The Binary (Base 2) is a numeral system that uses only two digits: 0 and 1. Each digit
in a binary number is called a bit (short for binary digit).
Features:
- Only two possible values for each digit (0 or 1).
- Each position represents a power of 2 (e.g., from right to left: 20, 21, 22, etc.).
- Example: The binary number 1011 represents:
1 * 23 + 0 * 22 + 1 * 21 + 1 * 20 = 8 + 0 + 2 + 1 = 11 in decimal.
Common Uses:
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Computing
The binary system is fundamental to digital computing, where data is processed as binary numbers by computers' hardware (using transistors for 0s and 1s).
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Storage
Binary is used in storage media, like hard drives and memory, to represent data.
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Logic Circuits
Used in digital electronics, including logic gates and circuits that perform mathematical operations.
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| Octal (Base 8) | The Octal (Base 8) numeral system, also known as the octal system, uses eight digits: 0, 1, 2, 3,
4, 5, 6 and 7. Each digit in an octal number represents a power of 8.
Features:
- Only eight possible digits (0 to 7) are used.
- Each position represents a power of 8 (e.g., from right to left: 80, 81, 82, etc.).
- Example: The octal number 17 represents:
1 * 81 + 7 * 80 = 8 + 7 = 15 in decimal.
Common Uses:
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Computing
Octal was historically used in computing as a shorthand for binary numbers. Each octal digit represents exactly three binary digits (bits).
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Digital Systems
It was used for compact representation of binary data in early computer systems, though hexadecimal (base-16) is more common today.
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Memory Addressing
In some older computer systems, octal was used for addressing and organizing data.
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| Decimal (Base 10) | The Decimal (Base 10) system is the base-10 numeral system, which uses ten digits: 0, 1, 2, 3, 4, 5,
6, 7, 8 and 9. It is the standard system for denoting integer and non-integer
numbers and is the most widely used number system in everyday life.
Features:
- Ten digits are used to represent all numbers.
- Each position in a decimal number represents a power of 10 (e.g., from right to left: 100, 101, 102, etc.).
- Example: The decimal number 345 represents:
3 * 102 + 4 * 101 + 5 * 100 = 300 + 40 + 5 = 345.
Common Uses:
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Everyday Life
The decimal system is the standard system used for counting, measuring and performing arithmetic in daily activities.
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Mathematics and Science
It is used universally in mathematics, engineering and scientific calculations.
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Currency
Most modern currencies are based on the decimal system.
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| Hexadecimal (Base 16) | The Hexadecimal (Base 16) number system uses sixteen digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B,
C, D, E, F, where A through F represent the values 10 to 15.
Features:
- Uses 16 distinct symbols (0 - 9 and A - F) to represent numbers.
- Each position represents a power of 16 (e.g., from right to left: 160, 161, 162, etc.).
- Example: The hexadecimal number 1A3 represents:
1 * 162 + A * 161 + 3 * 160 = 1 * 256 + 10 * 16 + 3 = 419 in decimal.
Common Uses:
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Computing
Hexadecimal is widely used in computing as a more compact representation of binary numbers. Every 4 bits (a nibble) correspond to 1 hexadecimal digit.
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Memory Addresses
It's used to represent memory addresses in programming, as it's more concise than binary and easier to read.
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Color Codes
In web development and design, hexadecimal codes are used to define colors (e.g., #FF5733).
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