Hamming Code Calculator
Hamming Code Calculator
Are you looking to generate errordetecting codes for your data? Stay here and use our Hamming Code Calculator. It is a tool that helps you create Hamming codes for error detection and correction. Enter your data bits and number of parity bits into the calculator to find the Hamming code.
How to Use the Calculator
To use the Hamming Code Calculator is easy. Follow these steps:
1. Enter the Data Bits (binary): Input your binary data bits.

 Example: Enter
1011
.
 Example: Enter
2. Select the Number of Parity Bits: Choose the number of parity bits required for your data bits.

 Example: Select
3
.
 Example: Select
After entering these values, click the “Calculate” button to generate the Hamming code.
What is Hamming Code?
Hamming code is an errordetecting and errorcorrecting code used in digital communication and computer memory. It adds redundancy to the data bits to detect and correct singlebit errors.
Formula
To calculate the Hamming code, follow these steps:

Determine the number of parity bits (p) needed for the data bits (m):
${2}^{p}\ge m+p+1$ 
Place the data bits and parity bits in their positions.

Calculate the values of the parity bits to ensure error detection and correction.
Variables
Variable  Description 

$m$  Number of data bits 
$p$  Number of parity bits 
$n$  Total number of bits (m + p) 
${d}_{i}$  Data bit at position $i$ 
${p}_{i}$  Parity bit at position $i$ 
How To Generate Errordetecting Codes
Example 1
 Data Bits:
1011
 Number of Parity Bits:
3
Calculation Steps:
1. Determine Total Bits:
Total bits $n=m+p=4+3=7$
2. Place Data Bits and Parity Bits:
Positions: 1 (p1), 2 (p2), 3 (d1), 4 (p3), 5 (d2), 6 (d3), 7 (d4)
Arrange: p1 p2 1 p3 0 1 1
Calculate Parity Bits:
$\mathrm{1.\; p}1$: Covers positions 1, 3, 5, 7


 $p1=1\oplus 0\oplus 1=0$

$\mathrm{2.\; p}2$: Covers positions 2, 3, 6, 7


 $p2=1\oplus 1\oplus 1=1$

$\mathrm{3.\; p}3$: Covers positions 4, 5, 6, 7


 $p3=0\oplus 1\oplus 1=0$

Result:
 The Hamming code is
0110101
.
Example 2
Foe example your inputs is,
 Data Bits:
1101
 Number of Parity Bits:
3
Calculation Step:
1. Determine Total Bits:

 Total bits $n=m+p=4+3=7$
2. Place Data Bits and Parity Bits:

 Positions: 1 (p1), 2 (p2), 3 (d1), 4 (p3), 5 (d2), 6 (d3), 7 (d4)
 Arrange:
p1 p2 1 p3 1 0 1
3. Calculate Parity Bits:
$\mathrm{1.\; p}1$: Covers positions 1, 3, 5, 7


 $p1=1\oplus 1\oplus 1=1$

$\mathrm{2.\; p}2$: Covers positions 2, 3, 6, 7


 $p2=1\oplus 0\oplus 1=0$

$\mathrm{3.\; p}3$: Covers positions 4, 5, 6, 7


 $p3=1\oplus 1\oplus 0\oplus 1=1$

4. Result:
 The Hamming code is
1011101
.
I hope you found our Hamming code calculator accurate. Please send us know your feedback. You can also report an error if you you are facing.