Error Detection/Correction Section 1.7 Section 3.9 Bonus Material: Hamming Code

ASCII Code

Format effector: control layout Communication Control Characters: frame a text message.

ASCII Examples ASCII A= ASCII T=

ASCII Code (Y) (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= – ASCII T= Odd Parity – ASCII A= – ASCII T=

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 are sent. 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.

Limitation of Parity Checking (1)

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

Two-terminal XOR

Gate Level Implementation of XOR

Alternative Implementation of XOR

Parity Generator The circuit that generates the parity bit in the transmitter is called a parity generator. (Truth Table)

Three-Terminal XOR

Four-Input Odd Function

Parity Error Check

Error Correction Hamming Code Use check bits to correct error

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

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 0C0C000C0C011C0C101C0C111C1C001C1C010C1C100C1C110C0C000C0C011C0C101C0C111C1C001C1C010C1C100C1C11

Generate the Second Check Bit 000C00 010C01 100C10 110C11 111C00 101C01 011C10 001C11

Generate the third Check Bit

Hamming Code Blue: Check bits Black: Data bits

Error in a Data Bit

Error in the Check Bit