Binary to Decimal Conversion
Binary (base 2) uses only 0 and 1. To convert binary to decimal, multiply each digit by 2 raised to its position power (starting from 0 on the right) and sum the results. Example: 1101 = 1×8 + 1×4 + 0×2 + 1×1 = 13.
Binary, Hex & Base Converter
Number base conversion is a daily skill for software engineers and computer scientists. Binary (base 2) is how CPUs process data at the hardware level; hexadecimal (base 16) is the standard notation for memory addresses, color codes (#FF5733), and byte values in debugging. Octal (base 8) appears in Unix file permissions (chmod 755). This converter handles bases 2 through 36, supports both integer and fractional parts, and shows the step-by-step positional conversion — making it useful for learning binary arithmetic, designing low-level systems, or decoding network packet data.
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Binary, Hex & Base Converter calculator
Decimal (Base 10)
Binary (Base 2)
1111
1111
Hex (Base 16)
FF
Octal (Base 8)
377
8-bit Visualization
1
1
1
1
1
1
1
1
128
64
32
16
8
4
2
1
lightbulb Tips
- •Binary is base-2 (0,1)
- •Hex is base-16 (0-9, A-F)
- •Octal is base-8 (0-7)
table_chart Quick Reference
Dec
Bin
Hex
Oct
0000000
1000111
81000810
151111F17
16100001020
25511111111FF377
How to Use the Binary, Hex & Base Converter
edit
Enter Your Number
Type the number you want to convert. Use 0x, 0b, or 0o prefixes for auto-detection.
input
Select Source Base
Choose the base of your input number, or use auto-detect.
output
Choose Target Base
Select which base(s) to convert to - single base or all common bases.
visibility
View Results
See your converted number with optional step-by-step explanation.
The Formula
To convert any base to decimal, multiply each digit by the base raised to its position power, then sum all values. For example, binary 1010 = 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10.
Value = Σ(digit × base^position)
lightbulb Variables Explained
- digit Each digit in the number (0-9, A-Z)
- base The number system base (2, 8, 10, 16, etc.)
- position Position from right, starting at 0
tips_and_updates Pro Tips
1
Use prefixes to quickly enter numbers: 0b for binary, 0o for octal, 0x for hexadecimal
2
Each hexadecimal digit equals exactly 4 binary digits - useful for quick mental conversion
3
When converting large numbers, work in groups of digits for easier calculation
4
Remember: A=10, B=11, C=12, D=13, E=14, F=15 in hexadecimal
5
Binary is fundamental - all other conversions go through binary internally in computers
Convert numbers instantly between binary, hexadecimal, octal, decimal, and any base from 2 to 36. Essential tool for programmers, students, and anyone working with different number systems.
Hexadecimal Conversion
Hexadecimal (base 16) uses 0-9 and A-F. It's popular in programming because each hex digit represents exactly 4 binary bits. FF in hex = 255 in decimal = 11111111 in binary.
Why Different Number Bases?
Computers use binary internally. Hexadecimal provides a compact way to represent binary data. Octal was used in older systems. Decimal is human-friendly. Each base has its purpose in computing and mathematics.