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Chapter 6 Exclusive-OR and Exclusive-NOR Gates 1

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6-1 The Exclusive-OR Gate The output is HIGH if either one or the other inputs are HIGH, but not both. 4

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The Exclusive-OR Gate Logic circuits for the exclusive-OR function. Logic Symbol and Boolean equation 5

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Figure 6-2 The Exclusive-OR Gate built with an AND-OR-NAND combination 6

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6-2 The Exclusive-NOR Gate The complement of the exclusive-OR. Often called an equality gate: The output is HIGH when the inputs are equal (both high or both low). 7

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The Exclusive-NOR Gate Ex-NOR Logic Circuit 8 EX-NOR Logic Symbol and Boolean equation

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6-3 Parity Generator / Checker Electrical noise in the transmission of binary information can cause errors. –0101 -> 0100 (the electrical noise present on the line during the transmission of the LSB may change 1 to 0) Parity can detect these types of errors. –Receiving device can signal an error condition or ask the transmitting device to retransmit. 10

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Parity systems Adds a bit to the binary information –4-bit system requires a 5 th bit, an 8-bit system needs a 9 th bit. Odd parity systems –The parity bit that is added must make the sum of all bits odd. Even parity systems –The parity bit that is added must make the sum of all bits even.

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Parity systems Parity generator –the circuit that creates the parity bit Parity checker –Determines if the received string is of the right parity on the receiving end The type of parity system and the location of parity bit (next to MSB or LSM) must be agreed on beforehand.

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Odd parity generator/checker 11 This scheme only detects errors that occur to 1 bit. The likelihood of 2 bits being affected is highly unusual.

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Four-bit even- and odd-parity generators 12

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Eight-bit even-parity generator 13

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Five bit even-parity checker 14

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Integrated-Circuit Parity Generator/Checker TTL IC logic symbol and Function Table 15

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17 Parity-Error Detection System

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Parallel Binary Comparator

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19 Controlled Inverter

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Discussion Point Does the circuit below function as an even or odd parity generator? 21

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Summary The exclusive-OR gate provides a HIGH output if one input or the other input, but not both, is HIGH. The exclusive-NOR gate outputs a HIGH if both inputs are HIGH or if both inputs are LOW. 24

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Summary A parity bit is commonly used for error detection during the transmission of digital signals. Exclusive-OR and exclusive-NOR gates are used in applications such as parity checking, binary comparison and controlled complementing circuits. FPGAs can be used to implement circuits containing the exclusive gates. 25

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