Binary Converter Calculator

The ultimate tool to convert numbers between binary decimal hexadecimal and octal with precision and flexible word sizes explore signed and unsigned views group bits instantly export results to CSV and PDF validate input in real time and understand two s complement math with clear steps plus helpful examples formatting batch mode for professionals

Enter Value
Spaces and underscores are ignored. Prefix signs supported for decimal.
Used for clamping and two’s complement.
Formula & Method

Key relationships used in this tool:

  • Binary → Decimal: If the bits are \(b_{n-1}\dots b_1 b_0\), the value is i=0..n-1 bi·2i.
  • Decimal → Binary: Repeatedly divide by 2 and collect remainders (or use base conversion).
  • Hex ↔ Binary: 1 hex digit = 4 bits. Group binary in nibbles to map directly.
  • Two’s Complement (signed n-bit): Unsigned range is 0 .. 2n−1; signed range is −2n−1 .. 2n−1−1. If the most significant bit is 1, the signed value equals unsigned − 2n.
  • Clamping: All conversions are reduced modulo 2n to honor the selected word size.
Conversion History
Timestamp Base Input Word Signed Binary Dec Unsigned Dec Signed Hex Oct
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Example Data

Sample 8‑bit conversions for quick reference.

DecimalBinaryHexOctalSigned (8‑bit)
50101555
151111F1715
310001 11111F3731
640100 00004010064
1270111 11117F177127
1281000 000080200-128
2001100 1000C8310-56
2551111 1111FF377-1
Tip: Use the Signed switch with a word size to interpret the same bit pattern as positive or negative using two’s complement.

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Binary to Octal Converter

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.