Tarife

Zahlensystem-Umrechner: Binär, Oktal, Dezimal und Hex

Dieser Umrechner wandelt eine ganze Zahl von einem Zahlensystem in ein anderes um — binär, oktal, dezimal, hexadezimal oder jede Basis von 2 bis 36. Er zeigt die Stellenwert-Rechnung und die wiederholte Division und prüft das Ergebnis durch Rückumwandlung.

Nur ganze Zahlen. Die Buchstaben A–Z sind die Ziffern 10–35.

Ergebnis

Gib Werte ein und tippe auf Berechnen, um das Ergebnis zu sehen.

Formel

(dk…d1d0)b=dkbk+⋯+d1b+d0(d_k \ldots d_1 d_0)_b = d_k b^k + \cdots + d_1 b + d_0

Each digit is multiplied by the base raised to the power of its position, starting at 0 on the right.

n÷b=q remainder rn \div b = q \text{ remainder } r

To convert from decimal, divide by the new base again and again; the remainders, read from last to first, are the digits.

So benutzt du diesen Rechner

  1. Type the number. For hexadecimal, use the letters A–F (upper or lower case).
  2. Choose the base it is written in and the base you want.
  3. Press Calculate to see the converted number, its decimal value and the working.

Gelöste Beispiele

255 in binary

Divide by 2 repeatedly: every remainder is 1, eight times.

Reading the remainders from bottom to top gives 11111111.

Binary 1011 to decimal

1 × 8 + 0 × 4 + 1 × 2 + 1 × 1 = 11.

255 in hexadecimal

255 ÷ 16 = 15 remainder 15, and 15 ÷ 16 = 0 remainder 15.

15 is the digit F, so 255 = FF.

Hexadecimal 1A3 to binary

1A3 = 1 × 256 + 10 × 16 + 3 = 419.

419 in binary is 110100011.

Häufige Fehler

  • Reading the remainders from top to bottom; the first remainder is the last (rightmost) digit.
  • Starting the place values at 1 instead of 0: the rightmost digit is multiplied by b⁰ = 1.
  • Using digits that do not exist in the base, such as 2 in binary or G in hexadecimal.

Häufig gestellte Fragen

How do you convert decimal to binary?

Divide by 2 and write down the remainder; repeat with the quotient until it is 0. Read the remainders from the last to the first. 13 → 1101.

How do you convert binary to decimal?

Multiply each digit by its place value (1, 2, 4, 8, … from the right) and add: 1011 = 8 + 0 + 2 + 1 = 11.

What are the letters in hexadecimal?

Hexadecimal needs 16 digits, so A–F stand for 10–15. FF = 15 × 16 + 15 = 255.