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## PowerPoint Slideshow about ' Error Detection/Correction ' - tanaya

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ASCII Examples

- ASCII A=1000001
- ASCII T=1010100

ASCII Code

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?

Parity Bit

- 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.

Examples of Parity Bit

- Even Parity
- ASCII A=01000001
- ASCII T=11010100
- Odd Parity
- ASCII A=11000001
- ASCII T=01010100

Signal Transmission Algorithm

- (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.

Parity Generator

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

(Truth Table)

Parity Checker

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

Hardware implementation

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

Two-terminal XOR

- 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:

Alternative Implementation of XOR

- (A’B’)’=A+B

Parity Generator

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

(Truth Table)

Three-Terminal XOR

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

Error Correction

- Hamming Code
- Use check bits to correct error

Add Check Bits

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

CC0C00

CC0C01

CC0C10

CC0C11

CC1C00

CC1C01

CC1C10

CC1C11

Generate the First Check Bit

0C0C00

0C0C01

1C0C10

1C0C11

1C1C00

1C1C01

0C1C10

0C1C11

Check bit 1 looks at bit 3 and bit 5.

Check bit 1=

Generate the Second Check Bit

000C00

010C01

100C10

110C11

111C00

101C01

011C10

001C11

Check bit 2 looks at bit 3 and bit 6.

Check bit 2=

Generate the third Check Bit

000000

010101

100110

110011

111000

101101

011110

001011

Check bit 4 looks at bit 6 and bit 5.

Check bit 4=

Error in a Data Bit

- 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!

Error in the Check Bit

- 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.

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