Konvertieren Numbers Between Radices

问题

You haben ein Zahl in one base (e.g., hex) und brauchen it in another (e.g., binary oder decimal) für ein unterschiedlich Werkzeug oder context.

Voraussetzungen

• Understanding of positional numeral systems
• Basic arithmetic

Schritte

1. 1. Identify the source and target radix

   Determine the base of your input number and the base you need as output. Common radices are 2 (binary), 8 (octal), 10 (decimal), and 16 (hex). The source value must be valid in its claimed base.

   Eingabe

   source: hex 1A | target: binary

   输出

   radices: 16 → 2

2. 2. Convert through decimal or directly

   The simplest method is to first parse the input as a decimal integer, then format that integer in the target base. For direct hex-to-binary, each hex digit maps to 4 bits without intermediate conversion.

   Eingabe

   1A (hex)

   输出

   26 (decimal) → 11010 (binary)

3. 3. Verify the result

   Convert the output back to the original base and confirm it matches the input. Check that no digits in the output exceed the target radix (e.g., no digit 8 in octal).

   Eingabe

   11010 (binary)

   输出

   1A (hex) ✓

Erwartetes Ergebnis

Der gleich numeric Wert represented in der target radix, mit alle digits gültig für das base.

Häufige Fehler

Using digits invalid for the source base

Hex allows A-F, but binary only allows 0-1. Validate the input before converting.

Losing leading zeros

Leading zeros are significant in fixed-width contexts like byte representations. Pad the output to the required width after conversion.

Troubleshooting指引

• If the result seems too large or small, double-check the source radix. A hex value read as decimal will be wrong.
• For fractional numbers, note that this tutorial covers integers only; fractional conversion requires separate handling.

Sicherheitsgrenzen

• Pure arithmetic conversion with no security implications.