Hamming codes (con’t)

• The check bits specify the error location

  • Check c1: It fails
    • Error is in one of bits 1,3,5,7,9,11,13,15
  • Check c2: It fails
    • Error is in one of bits 3,7,11,15
  • Check c3: It passes
    • Error is in one of bits 3,11
  • Check c4: It passes
    • Error is in bit 3

• The parity-check bits are called a syndrome

  • The syndrome tells us the location of the error

Position in message

binary decimal

0001 1

0010 2

0011 3

0100 4

0101 5

0110 6

0111 7

1000 8

1001 9

1010 10

1011 11

1100 12

1101 13

1110 14

1111 15

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