Binary Converter
Convert between decimal, binary, and hexadecimal number systems
How Binary Conversion Works
Understanding number system conversions
Converting Decimal to Binary
To convert a decimal number to binary:
- Divide the decimal number by 2.
- Get the integer quotient for the next iteration.
- Get the remainder for the binary digit.
- Repeat the steps until the quotient becomes 0.
- The binary equivalent is the sequence of remainders read from bottom to top.
Example: Converting 25 to Binary
25 ÷ 2 = 12 remainder 1
12 ÷ 2 = 6 remainder 0
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Binary result (reading remainders from bottom to top):
11001
Hexadecimal Conversion
Hexadecimal (base-16) uses digits 0-9 and letters A-F (where A=10, B=11, ..., F=15). It's commonly used in computing as a more concise way to represent binary data, where each hex digit represents 4 binary digits.
Binary 1010 1101 = Hex AD (because 1010 = A and 1101 = D)
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About Binary Numbers
Understanding binary and its applications
Binary is a base-2 number system that uses only two digits: 0 and 1. It's the fundamental language of computers and digital systems.
In binary, each position represents a power of 2, starting from the rightmost digit (2⁰ = 1) and increasing as you move left (2¹ = 2, 2² = 4, 2³ = 8, etc.).
Binary is essential in computing because electronic components can easily represent two states: on/off, high/low voltage, or magnetized/demagnetized.
Number Systems
- Decimal (Base-10):0-9
- Binary (Base-2):0-1
- Octal (Base-8):0-7
- Hexadecimal (Base-16):0-9, A-F