Convert between Binary, Octal, Decimal and Hexadecimal
A numeral system (or system of numeration) is a writing system for expressing numbers using digits or other symbols in a consistent manner. Different base systems are widely used in computer science, electrical engineering, and mathematics.
Uses two symbols: 0 and 1. It's the foundation of computer systems - all data is ultimately stored and processed in binary form.
Uses eight symbols: 0-7. Often used in computing as a shorthand for binary, with each octal digit representing three binary bits.
Uses ten symbols: 0-9. The most common numbering system in daily life and the international standard for numerical representation.
Uses sixteen symbols: 0-9 and A-F. Widely used in computing, with each hex digit representing four binary bits, ideal for memory addresses and color codes.
In programming, developers frequently work with different number bases for memory addresses, bitwise operations, color values, etc.
Understanding computer fundamentals like data storage and instruction sets requires knowledge of number base conversions.
Learning numeral systems is an important part of mathematics education, helping to understand the nature of numerical representation.
Q: Why do computers use binary?
A: Computers use binary because electronic devices can most easily represent and distinguish between two states (on/off, high voltage/low voltage), making binary the most natural and reliable foundation for computer systems.
Q: What do the letters in hexadecimal represent?
A: Hexadecimal uses A-F to represent decimal values 10-15. A=10, B=11, C=12, D=13, E=14, F=15.
Q: How to convert fractional parts between bases?
A: Fractional part conversion uses the "multiply by base" method. Multiply the fractional part by the target base, take the integer part as a result digit, then continue with the new fractional part.
Q: How are negative numbers handled in base conversion?
A: Negative number conversion typically involves converting the absolute value first, then adding sign information according to the number representation method (like signed magnitude, one's complement, two's complement). In computers, negatives are usually represented in two's complement form.
Master these techniques to improve base conversion efficiency and accuracy: