🎓 Computer Science • Number Systems
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Decimal Converter (Base 10 ⇄ Binary, Hex, Oct)
Converts base-10 decimal numbers into binary, hexadecimal, and octal with step-by-step successive division remainders.
Presets:
Interactive Register Bit-Strip (Click Bits to Toggle)
Decimal (Base 10)
255
Signed 8-bit: -1 | Signed 16-bit: 255
Binary (Base 2)
1111 1111
Prefix:
0b11111111Hexadecimal (Base 16)
0xFF
Nibbles: F F
Octal (Base 8) & ASCII
0o377
ASCII Char: Non-printable
Positional Weight Expansion (Base 2)
(1 × 2^7 = 128) + (1 × 2^6 = 64) + (1 × 2^5 = 32) + (1 × 2^4 = 16) + (1 × 2^3 = 8) + (1 × 2^2 = 4) + (1 × 2^1 = 2) + (1 × 2^0 = 1) = 255
What is the Decimal System?
The decimal numeral system is the standard base-10 system used by humans, using digits 0 through 9.
Formula & Step-by-Step Calculation
Divide successively by target radix b; remainders give digits from right to left.
Euclidean division algorithm for base conversion.
Worked Step-by-Step Examples
Example 1
Convert decimal 255 to hexadecimal and binary
Solution: 0xFF and 11111111₂
• 255 / 16 = 15 R 15 (F) ⟹ 0xFF; 255 in binary = 11111111
Common Real-World & Academic Use Cases
- ✓ Programming integer format specification
- ✓ Web color code conversion (RGB to Hex)
- ✓ Assembly language immediate value encoding
How to Use the Decimal Converter (Base 10 ⇄ Binary, Hex, Oct)
1
Enter Decimal Integer
Type base-10 value.
2
View Converted Radices
Review binary, hex, and octal equivalents.
Frequently Asked Questions
Q: What is the largest value in an 8-bit unsigned integer?
255 (2⁸ - 1), represented as 0xFF in hex or 11111111 in binary.