Zahlensystem-Umrechner

Rechnen Sie Zahlen zwischen verschiedenen Basen um. Binär, Oktal, Dezimal, Hexadezimal.

Decimal Number

Rem 2

Rem 87

Rem 1615

Log16 Val2

Formel anzeigen →

Formel

Number Base Conversion

Method: Repeated Division

To convert decimal to base b: 1. Divide n by b, record the remainder 2. Replace n with the quotient 3. Repeat until n = 0 4. Read remainders from bottom to top

Common Bases

Binary (base-2): 0, 1

Octal (base-8): 0-7

Decimal (base-10): 0-9

Hexadecimal (base-16): 0-9, A-F

Lösungsbeispiel

Analyze the number 255 in different bases.

01255 in binary: 11111111 (8 binary digits)
02255 in octal: 377 (last digit: 255 mod 8 = 7)
03255 in hex: FF (last digit: 255 mod 16 = 15 = F)
04Bits needed: floor(log2(255))+1 = 8

Häufig Gestellte Fragen

Why are number bases important?

Different bases are used in different contexts: binary for computers, octal for Unix permissions, hexadecimal for memory addresses and colors, decimal for everyday use.

How do I convert from decimal to binary?

Repeatedly divide by 2 and record remainders. Read the remainders from bottom to top. For example, 13 → 6r1 → 3r0 → 1r1 → 0r1, so 13 = 1101 in binary.

Why is 255 special in computing?

255 is the largest 8-bit unsigned integer (11111111 in binary, FF in hex). It is the maximum value for each channel in 24-bit RGB color codes.

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