DIGITAL · TOOL

Hamming Code Calculator

Data ⇄ codeword + single-error detection and correction — the syndrome locates the faulty bit.

Basic No backend · 100% client-side

What it does: Encode Hamming code, or detect and correct a single-bit error in a received codeword.

When to use it: When learning error-correcting codes or working on communication/storage reliability.

Data bits^?

→ 7-bit codeword

Parity Bit Calculator

Even/odd parity bit from the count of 1s

CRC Calculator

CRC-8/16/32 checksums from text or hex

Number Base Converter

Binary/octal/decimal/hex — type once, all four stay in sync

How to

How to use the Hamming code calculator

Pick a mode and enter a 0/1 string.

01

Pick a mode

Encode (data → codeword) or Decode / correct (codeword → detect and fix errors).
02

Enter a 0/1 string

For encoding, type the data bits (e.g. 1011); for decoding, type the received codeword.
03

Read the result

Encoding gives the full codeword; decoding gives the syndrome, error position and the corrected codeword.

FAQ

How many errors can Hamming code correct?

A basic SEC Hamming code corrects 1 bit error. The value of the syndrome is exactly the position of the faulty bit; 0 means no error.

Where do the parity bits go?

At positions 1, 2, 4, 8… (powers of two); data fills the remaining positions. In this tool, positions are counted from 1 starting at the left.

What happens with a 2-bit error?

A basic Hamming code cannot tell them apart and will mis-correct another bit. Detecting 2-bit errors needs SECDED (one extra overall parity bit).

How is the syndrome computed?

Each parity bit checks even parity over the bits it covers; summing the position values of the failing parity bits gives the error position.

Data Provenance

Item	Value / Formula	Source
Hamming SEC	`Parity bits at 2^k positions`	Hamming (1950)

Classic Hamming SEC algorithm, no external API.