1. Combinational Logic Design
Parity Generator & Checker

2. Parity Generator/Checkers - XOR &XNOR Revision - Application of XOR&XNOR gates - Parity System - Parity Generator Design - Parity Checker Design - Parity Generator/Checker Chip

3. A X A X
The XOR Gate B B
The XOR gate produces a HIGH output only when the inputs are at opposite logic levels. The truth table is
0 0
0 1
1 0
1 1 1
-XOR gate has only two inputs.
-The “circle-OR” symbol doesn’t appear in any of our Boolean rules, so if you’re doing a Boolean derivation, write out the longer form shown above for XORs.
The XOR operation is written as X = AB + AB. Alternatively, it can be written with a circled plus sign between the variables as X = A + B.

4. The XNOR operation can be written as X = AB + AB or as X = A + B.
The XNOR Gate B B
The XNOR gate produces a HIGH output only when the inputs are at the same logic level. The truth table is
0 0
0 1
1 0
1 1 1
-XNOR gate has only two inputs.
-As noted earlier, the “circle-OR” symbol doesn’t appear in any of our Boolean rules, so if you’re doing a Boolean derivation, write out the longer form shown above.
The XNOR operation can be written as X = AB + AB or as X = A + B.

5. Applications of XOR and XNOR Gates
Three common applications:
Comparators
Controlled inverters
Parity generation and checking

6. Example Solution Application #3: Parity Checking
Parity checking is a method of error detection for simple transmission errors involving one bit. A parity bit is an “extra” bit attached to a group of bits to force the total number of 1’s to be either even (even parity) or odd (odd parity).
The ASCII character for “a” is and for “A” is What is the correct bit to append to make both of these have odd parity?
Example
Recall ASCII table on p. 19.
Solution
The ASCII “a” has an odd number of bits that are equal to 1; therefore the parity bit is 0. The ASCII “A” has an even number of bits that are equal to 1; therefore the parity bit is 1.

7. ODD Parity
In ODD parity, when we add the bits together disregarding weight we get or want to get an odd number.
is a four bit message add a parity bit to make it odd
Odd parity is satisfied
is an eight bit message add a parity bit to make it odd
Odd parity is satisfied
Parity bit

8. EVEN parity
In EVEN parity when we add the bits together disregarding weight we get or want to get an even number.
is a four bit message add a parity bit to make it even
Even parity is satisfied
is an eight bit message add a parity bit to make it even
Even parity is satisfied
Parity bit

9. Parity System (8 bit input)

10. Parity Generator (3 bit input)
* For odd parity, the bit P is generated so as to make the number of 1’s odd (including P)
X Y Z P

11. Parity System (8 bit input)

12. Parity Checker
The three-bit message and parity bit are transmitted to their destination, where they are applied to a parity checker circuit.
An error occurs during transmission if the parity of the four bits is even, since the binary info transmitted was originally odd.
The output C of the parity checker should be a 1 when an error occurs, i.e. when the number of 1’s in the four inputs is even.
X Y Z P C

13. Error-Detection
Parity is used in digital circuits to check for errors in transmission.
In Four bit transmission a parity bit is added to make the fifth bit.
In a eight bit transmission a parity bit is added to made a ninth bit.…..and so on.

14. Parity Generators
To implement parity checking, we need circuitry on the transmitter that generates the parity bit for each group of bits being sent. This circuitry is called a parity generator.
Next slide shows how to build 4-bit even or odd parity generators.

15. How to design Parity Generators
Use exclusive ORs and Exclusive NORs

16. Parity Checkers
On the receiver, we need circuitry that checks the data bits and parity bit as they’re received to decide whether an error has occurred during transmission. This circuitry is called a parity checker.
Next slide shows how to build a 4-bit-plus-parity even parity checker.

17. How to design Parity Checker

18. How to design a parity checker

19. Odd or even parity 0 out of a parity checker means the parity
checks and all is ok
-1 out of a parity checker means there is an error

20. Parity Generator/Checker Chip
The can be used to generate a parity bit or to check an incoming data stream for even or odd parity.
Checker: The can test codes with up to 9 bits. The even output will be HIGH if the data lines have even parity; otherwise it will be LOW. Likewise, the odd output will be HIGH if the data lines have odd parity; otherwise it will be LOW.
Data inputs
S Even
S Odd
Generator: To generate even parity, the parity bit is taken from the odd parity output. To generate odd parity, the output is taken from the even parity output.
74280

21. The End