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Understanding Exclusive-OR and Exclusive-NOR Gates: Applications in Parity Checking

This chapter delves into Exclusive-OR (XOR) and Exclusive-NOR (XNOR) gates, fundamental elements in digital logic. The XOR gate outputs HIGH when one input is HIGH, while the XNOR gate outputs HIGH when both inputs are equal. These gates are crucial in constructing parity generators and checkers to detect errors during binary information transmission. The chapter also discusses odd and even parity systems, parity bit generation, and applications in error detection and binary comparison, emphasizing their role in ensuring the integrity of digital signals.

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Understanding Exclusive-OR and Exclusive-NOR Gates: Applications in Parity Checking

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  1. Chapter 6 Exclusive-OR and Exclusive-NOR Gates 1

  2. 6-1 The Exclusive-OR Gate • The output is HIGH if either one or the other inputs are HIGH, but not both. 4

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

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

  5. 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

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

  7. 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

  8. 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.

  9. 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.

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

  11. Four-bit even- and odd-parity generators 12

  12. Eight-bit even-parity generator 13

  13. Five bit even-parity checker 14

  14. Integrated-Circuit Parity Generator/Checker • 74280 TTL IC logic symbol and Function Table 15

  15. Parity-Error Detection System 17

  16. Parallel Binary Comparator

  17. Controlled Inverter 19

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

  19. 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

  20. 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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