Chapter 6

Exclusive-OR and Exclusive-NOR Gates

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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.

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The Exclusive-OR Gate

Logic circuits for the exclusive-OR function.

Logic Symbol and Boolean equation

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

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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).

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The Exclusive-NOR Gate

Ex-NOR Logic Circuit

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EX-NOR Logic Symbol and Boolean equation

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.

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Parity systems

• Adds a bit to the binary information– 4-bit system requires a 5th bit, an 8-bit system

needs a 9th 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.

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.

Odd parity generator/checker

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• This scheme only detects errors that occur to 1 bit.• The likelihood of 2 bits being affected is highly

unusual.

Four-bit even- and odd-parity generators

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Eight-bit even-parity generator

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Five bit even-parity checker

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Integrated-Circuit Parity Generator/Checker

• 74280 TTL IC logic symbol and Function Table

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Parity-Error Detection System

Parallel Binary Comparator

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Controlled Inverter

Discussion Point• Does the circuit below function as an even

or odd parity generator?

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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.

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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.

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