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Chapter 6

Chapter 6. Exclusive-OR and Exclusive-NOR Gates. 1. 6-1 The Exclusive-OR Gate. The output is HIGH if either one or the other inputs are HIGH, but not both . 4. The Exclusive-OR Gate. Logic circuits for the exclusive-OR function . Logic Symbol and Boolean equation. 5.

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Chapter 6

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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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