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Error Detection/Correction PowerPoint Presentation

Error Detection/Correction

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Error Detection/Correction

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Error Detection/Correction

Section 1.7

Section 3.9

Bonus Material: Hamming Code

Communication

Control

Characters: frame a text message.

Format effector:

control layout

- ASCII A=1000001
- ASCII T=1010100

1011001 (Y)

1001110 (N)

If the probability of a bit flipping event is 1%,

what is the likely hood that 4 bits are flipped simultaneously?

- ASCII characters are stored one per byte (8 bits)
- The leftmost bit is called the parity bit
- A parity bit is an extra bit included with a message to make the total number of 1’s either even or odd.

- Even Parity
- ASCII A=01000001
- ASCII T=11010100

- Odd Parity
- ASCII A=11000001
- ASCII T=01010100

- (Even Parity System)
- A parity bit is generated and attached to the raw data
- An eight-bit sequence including the parity bit aresent.
- The parity of each character is checked at the receiving end.
- If the parity of the received character is not even, then at least one bit has changed value during transmission. The sender must retransmit the signal.

- The circuit that generates the parity bit in the transmitter is called a parity generator.

(Truth Table)

- The Circuit that checks the parity in the receiver is called a parity checker.

(1)

(1)

- Review of two-terminal XOR/XNOR
- Three terminal XOR/XNOR
- Hardware Implementation

- Equal to 1 if x and y differ in value
- Alternative description: equal to 1 if an odd number of variables equal to 1
- Characteristics:

- (A’B’)’=A+B

- The circuit that generates the parity bit in the transmitter is called a parity generator.

(Truth Table)

- equal to 1 if there is an odd number of variables equal to 1

Since , if P=0,

the same circuit can be used

as a 3-bit even parity generator.

zP

- Hamming Code
- Use check bits to correct error

Notation: (bit 1, bit 2, bit 3)

000

001

010

011

100

101

110

111

Notation: (bit 1, bit 2, bit 3, bit 4, bit 5, bit 6)

CC0C00

CC0C01

CC0C10

CC0C11

CC1C00

CC1C01

CC1C10

CC1C11

0C0C00

0C0C01

1C0C10

1C0C11

1C1C00

1C1C01

0C1C10

0C1C11

Check bit 1 looks at bit 3 and bit 5.

Check bit 1=

000C00

010C01

100C10

110C11

111C00

101C01

011C10

001C11

Check bit 2 looks at bit 3 and bit 6.

Check bit 2=

000000

010101

100110

110011

111000

101101

011110

001011

Check bit 4 looks at bit 6 and bit 5.

Check bit 4=

000000

010101

100110

110011

111000

101101

011110

001011

Blue: Check bits

Black: Data bits

- Data Bit: 100
- 111000
- Error occurs in the 6th bit, we get 111001 instead.
- Expected check bit 1:. OK
- Expected check bit 2:. Problem!
- Expected check bit 4:. Problem!
- The bad bit is 2+4=6!

- Data Bit: 100, Check Bit: 110
- 111000 (No error)
- Error occurs in the 1thbit, we get 011000instead.
- Expected check bit 1:. Problem!
- Expected check bit 2:. OK
- Expected checkbit 4:. OK
- The bad bit is bit number 1.