### lec8

```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
Figure 6-2 The Exclusive-OR Gate built
with an AND-OR-NAND combination
6
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
The Exclusive-NOR Gate
Ex-NOR Logic Circuit
EX-NOR Logic Symbol and Boolean equation
8
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
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
• This scheme only detects errors that occur to 1 bit.
• The likelihood of 2 bits being affected is highly
unusual.
11
Four-bit even- and odd-parity
generators
12
Eight-bit even-parity generator
13
Five bit even-parity checker
14
Integrated-Circuit Parity
Generator/Checker
• 74280 TTL IC logic symbol and Function
Table
15
Parity-Error Detection System
17
Parallel Binary Comparator
Controlled Inverter
19
Discussion Point
• Does the circuit below function as an even
or odd parity generator?
21
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
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
```