Binary to Decimal Converter
Convert binary numbers to human-readable decimals instantly. Supports arbitrary-precision integers (BigInteger) for networking and digital logic tasks, with spacing toggles for readability.
About
Converting between base-2 (binary) and base-10 (decimal) is a fundamental operation in computer science, essential for understanding IP addressing (e.g., IPv4 masks), subnetting, and low-level memory allocation. Errors in this translation can lead to incorrect addressing or buffer overflows. This tool provides a reliable conversion mechanism capable of handling integers far exceeding the standard 64-bit limitation, utilizing arbitrary-precision logic to support inputs of virtually any length.
Visual ergonomics are addressed via a spacing toggle, breaking dense binary streams into 4-bit or 8-bit blocks to reduce cognitive load and eye strain during manual verification. The validation engine ensures that only valid bit sequences are processed, rejecting malformed inputs instantly.
Formulas
A binary number dn...d1d0 is converted to decimal D by summing the powers of 2 for each bit position where the digit is 1.
D = n∑i=0 di × 2i
Example: Binary 1011 to Decimal
= (1 × 23) + (0 × 22) + (1 × 21) + (1 × 20)
= 8 + 0 + 2 + 1 = 11
Reference Data
| Power of 2 | Decimal Value | Binary Representation |
|---|---|---|
| 20 | 1 | 1 |
| 21 | 2 | 10 |
| 22 | 4 | 100 |
| 23 | 8 | 1000 |
| 24 | 16 | 0001 0000 |
| 27 | 128 | 1000 0000 (Most Sig. Bit in Byte) |
| 28 | 256 | 1 0000 0000 |
| 210 | 1024 | 100 0000 0000 (1 KB approximation) |
| 216 | 65535 | 1111 1111 1111 1111 (Max 16-bit uint) |
| 232 | 4294967296 | 1 followed by 32 zeros |