XOR

1
XOR

• XOR True (1) if there is an odd number of 1s
• XOR False (0) if an even number of 1s

2
Parity Values

• Supplementary Slideset
• (Best viewed individually)

3
Parity Example

• 10101010 . 01010101 . 11100010
• Parity XOR(1,0,1) 0
• XOR(0,1,1) 0
• XOR(1,0,1) 0
• XOR(0,1,0) 1
• XOR( 1,0,0) 1
• XOR(0,1,0) 1
• XOR(1,0,1) 0
• XOR(0,1,0) 1

4
Parity Recovery

• 10101010 . 01010101 .
• Parity 00011101
• 11100010

5
Initial Numbers

• Four bytes
• 10101010
• 01010101
• 11110000
• 00110001

6
First Parity Bit

• First bit of each
• 1, 0, 1, 0
• Even number
• Parity is 0

7
Second Parity Bit

• Second bit of each
• 0, 1, 1, 0
• Even number
• Parity is 0

8
Third Parity Bit

• Third bit of each
• 1, 0, 1, 1
• Odd number
• Parity is 1

9
Fourth Parity Bit

• 0, 1, 1, 1
• Odd number
• Parity is 1

10
Fifth Parity Bit

• 1, 0, 0, 0
• Odd Number
• Parity is 1

11
Sixth Parity Bit

• 0, 1, 0, 0
• Odd Number
• Parity is 1

12
Seventh Parity Bit

• 1, 0, 0, 0
• Odd Number
• Parity is 1

13
Eigth Parity Bit

• 0, 1, 0, 1
• Even Number
• Parity is 0

14
Regenerating

• To regenerate a lost value
• Find the parity of the remaining bits
• Partial-parity
• For each bit of Parity
• If the Partial-parity bit is the same
• Same number of ones before/after, value is a 0
• If Partial-parity is different
• Different number of ones before/after, value is a
  1

15
Recover Bit 1

• 1, 1, 0
• Partial-parity 0
• Parity 0
• Value is 0

16
Recover Bit 2

• 0, 1, 0
• Partial Parity 1
• Parity 0
• Value is a 1

17
Recover Bit 3

• 1, 1, 1
• Partial-parity is 1
• Parity is 1
• Value is 0

18
Recover Bit 4

• 0, 1, 1
• Partial-parity is 0
• Parity is 1
• Value is 1

19
Recover Bit 5

• 1, 0 ,0
• Partial Parity is 1
• Parity is 1
• Value is 0

20
Recover Bit 6

• 0,0,0
• Partial-parity is 0
• Parity is 1
• Value is 1

21
Recover Bit 7

• 1, 0, 0
• Partial-parity is 1
• Parity is 1
• Value is 0

22
Recover Bit 8

• 0, 0, 1
• Partial-parity is 1
• Parity is 0
• Value is 1

23
Recover Bit 1

• 1, 0, 0
• Partial-parity is 1
• Parity is 0
• Value is 1

24
Recover Bit 2

• 0, 1, 0
• Partial-parity is 1
• Parity is 0
• Value is 1

25
Recover Bit 3

• 1, 0, 1
• Partial-parity is 0
• Parity is 1
• Value is 1

26
Recover Bit 4

• 0, 1, 1
• Partial-parity is 0
• Parity is 1
• Value is 1

27
Recover Bit 5

• 1, 0, 0
• Partial-parity is 1
• Parity is 1
• Value is 0

28
Recover Bit 6

• 0, 1, 0
• Partial-parity is 1
• Parity is 1
• Value is 0

29
Recover Bit 7

• 1, 0, 0
• Partial-parity is 1
• Parity is 1
• Value is 0

30
Recover Bit 8

• 0, 1, 1
• Partial-parity is 0
• Parity is 0
• Value is 0