Enter a number, source base, and target base for instant conversion (supports 2~36 bases)
Input Number
Source Base
Target Base
Result
Conversion Result
Step-by-Step Derivation
Base Conversion Principle
① Other base → Decimal: Expand by place value and sum
② Decimal → Other base: Repeated division (reverse order of remainders)
③ Direct base conversion: Use decimal as intermediate bridge
Base conversion is a fundamental skill in computer science. Numbers in different bases are simply different representations of the same value.
⚠Each digit of the input must be less than the source base. For example, binary can only contain 0 and 1. Digits greater than 9 are represented by A~Z (10~35). Maximum supported base is 36.
What Is Base Conversion?
A number base (or radix) defines the digit set used in a counting system. Common bases include binary (2), octal (8), decimal (10), and hexadecimal (16). Base conversion expresses the same numeric value in a different base.
Place Value Expansion
Any base to decimal: multiply each digit by the base raised to its position, then sum. For example, binary 101 = 1×2²+0×2¹+1×2⁰ = 5.
Repeated Division
Decimal to other base: repeatedly divide by the target base, collecting remainders. Read from the last quotient backward through all remainders.
Digits & Letters
Values 10~35 are represented by A~Z respectively. For example, in hexadecimal, 10=A, 11=B, 15=F. Bases higher than 10 use letters.
Applications
Programming uses hexadecimal for memory addresses and color values; octal for file permissions; binary for low-level algorithm design.
💡 Teaching Example: Convert binary 1101 to decimal. Expand by place value: 1×2³+1×2²+0×2¹+1×2⁰ = 8+4+0+1 = 13. So 1101₂ = 13₁₀.
How do you convert between different number bases?▼
The core method: first convert to decimal (expand by place value), then convert from decimal to the target base (repeated division). For example, binary→decimal: multiply each digit by its power of 2 and sum; decimal→hexadecimal: repeatedly divide by 16 and collect remainders.
Why do computers commonly use binary, octal, and hexadecimal?▼
Computers use binary internally (0 and 1) because electronic circuits have only on/off states. Octal and hexadecimal are compact representations of binary: 1 octal digit = 3 binary digits, 1 hex digit = 4 binary digits, making them easier to read and write.
How do you convert binary to decimal?▼
Expand by place value and sum: from right to left, multiply each digit by its power of 2 (starting from 2^0), then add them up. For example, 1101₂ = 1×2³+1×2²+0×2¹+1×2⁰ = 8+4+0+1 = 13₁₀.
How do you convert decimal to hexadecimal?▼
Repeatedly divide by 16 and collect remainders from last to first. Digits 10~15 are represented by A~F. For example, 255÷16=15 remainder 15(F), 15÷16=0 remainder 15(F), so 255₁₀ = FF₁₆.
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