Hamming (7,4)

A hamming code that takes 4 input bits and produces 7 output bits that are ECC. It is a 1-bit ECC.

Process

Drawing 2025-05-30 11.26.23.excalidraw

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Text Elements

1

2

3

x1

x3

x2

x4

P1

P2

P3

Location

Label

x1

x2

x3

x4

P1

P2

P3

L1 = (1,1,1)

L2 = (1,0,1)

L3 = (1,1,0)

L4 = (0,1,1)

L5 = (1,0,0)

L6 = (0,1,0)

L7 = (0,0,1)

Link to original

• Takes 4-bit string $x=(x_1,x_2,x_3,x_4)$
• Creates 3 parity bits $P_1,P_2,P_3$
• Align each $P_i$ such that the String Parity within each circle is 1
• If the entries in the $i-th$ circle sum to 1, $P_i=1$, otherwise $P_i=0$