Base Conversion
Base conversion refers to the process of converting a number from one numeral system (or base) to another. The most commonly used numeral systems are:
- Decimal (Base 10): This is the standard system we use in everyday life.
- Binary (Base 2): Used in computer science, representing numbers using only 0 and 1.
- Octal (Base 8): Uses digits from 0 to 7.
- Hexadecimal (Base 16): Uses digits from 0 to 9 and letters A to F, where A stands for 10, B for 11, and so on.
Common Base Systems
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Decimal (Base 10): Uses digits 0 through 9.
- Example: 35410354_{10} 354 10
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Binary (Base 2): Uses digits 0 and 1.
- Example: 1101102110110_2 110110 2
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Octal (Base 8): Uses digits 0 through 7.
- Example: 4538453_8 453 8
-
Hexadecimal (Base 16): Uses digits 0-9 and letters A-F.
- Example: 1A3F161A3F_{16} 1A3F 16
Base Conversion: Common Methods
1. Decimal to Binary Conversion
To convert a decimal number (base 10) to binary (base 2), use the following method:
- Divide the decimal number by 2.
- Write down the remainder.
- Divide the quotient obtained in step 1 by 2, and repeat the process until the quotient becomes 0.
- The binary number is the sequence of remainders read from bottom to top.
Example: Convert 13 to binary:
- 13÷2=613 \div 2 = 6 13 ÷ 2 = 6 remainder 1
- 6÷2=36 \div 2 = 3 6 ÷ 2 = 3 remainder 0
- 3÷2=13 \div 2 = 1 3 ÷ 2 = 1 remainder 1
- 1÷2=01 \div 2 = 0 1 ÷ 2 = 0 remainder 1
Reading the remainders from bottom to top: 1310=1101213_{10} = 1101_2 13 10 = 1101 2