Convert numbers between binary, decimal, hexadecimal, and octal systems. Learn number theory with interactive tools and step-by-step explanations.
Step-by-step guides for converting between different number systems
Interactive calculators for instant number system conversions
Understand the fundamentals of number systems and their applications
Used in digital circuits and computer systems. Fundamental to computing.
The standard system for everyday counting and mathematics.
Compact representation of binary data. Used in programming and web design.
Historical importance in computing. Sometimes used in file permissions.
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Binary uses base-2 (0,1), decimal uses base-10 (0-9), and hexadecimal uses base-16 (0-9,A-F). Each system has different applications: binary for computers, decimal for everyday use, and hexadecimal for compact representation of binary data.
Computers use binary because electronic circuits can easily represent two states: on/off, high/low voltage, or magnetic polarity. This makes binary the most reliable and efficient system for digital electronics.
To convert decimal to binary, repeatedly divide the number by 2 and record the remainders. The binary equivalent is the remainders read in reverse order. For example, 13 in decimal: 13÷2=6 rem1, 6÷2=3 rem0, 3÷2=1 rem1, 1÷2=0 rem1 → 1101 in binary.
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