Title: Parity generator & Checker Practical Based on VHDL Programming
Aim: To design and verify the truth table of a three bit Odd Parity generator and checker.
Objectives:
- To study the VHDL programming language.
- To study the Parity generator & Checker.
Software & Hardware Requirement:
- Minimum Pentium 4, 512 MB RAM & 40 HDD.
- Xilinx software version 9.1v.
Theory of Parity Generator: A parity bit is used for the purpose of detecting errors during transmission of binary information. A parity bit is an extra bit included with a binary message to make the number of 1’s either odd or even. The message including the parity bit is transmitted and then checked at the receiving end for errors. An error is detected if the checked parity does not correspond with the one transmitted. The circuit that generates the parity bit in the transmitter is called a parity generator and the circuit that checks the parity in the receiver is called a parity checker.
In even parity the added parity bit will make the total number of 1’s an even amount and in odd parity the added parity bit will make the total number of 1’s an odd amount.
In a three bit odd parity generator the three bits in the message together with the parity bit are transmitted to their destination, where they are applied to the parity checker circuit. The parity checker circuit checks for possible errors in the transmission. Since the information was transmitted with odd parity the four bits received must have an odd number of 1’s. An error occurs during the transmission if the four bits received have an even number of 1’s, indicating that one bit has changed during transmission. The output of the parity checker is denoted by PEC (parity error check) and it will be equal to 1 if an error occurs, i.e., if the four bits received has an even number of 1’s.
ODD PARITY GENERATOR:
TRUTH TABLE:
Sr.No | INPUT
Three Bit Message |
OUTPUT
Odd Parity Bit |
||
A | B | C | P | |
1 | 0 | 0 | 0 | 1 |
2 | 0 | 0 | 1 | 0 |
3 | 0 | 1 | 0 | 0 |
4 | 0 | 1 | 1 | 1 |
5 | 1 | 0 | 0 | 0 |
6 | 1 | 0 | 1 | 1 |
7 | 1 | 1 | 0 | 1 |
8 | 1 | 1 | 1 | 0 |
From the truth table the expression for the output parity bit is,
P (A, B, C) = Σ (0, 3, 5, 6)
K-Map for Parity Generator:
0 | 1 | ||
C | C | ||
00 | AB | 1 | 0 |
01 | AB | 0 | 1 |
11 | AB | 1 | 0 |
10 | AB | 0 | 1 |
Also written as, P = A’B’C’ + A’BC + AB’C + ABC’ = (A EXOR B EXOR C)
ODD PARITY CHECKER:
TRUTH TABLE:
Sr.No | INPUT
Four Bit Message Recived |
OUTPUT
Parity error check |
|||
A | B | C | P | X | |
1 | 0 | 0 | 0 | 0 | 1 |
2 | 0 | 0 | 0 | 1 | 0 |
3 | 0 | 0 | 1 | 0 | 0 |
4 | 0 | 0 | 1 | 1 | 1 |
5 | 0 | 1 | 0 | 0 | 0 |
6 | 0 | 1 | 0 | 1 | 1 |
7 | 0 | 1 | 1 | 0 | 1 |
8 | 0 | 1 | 1 | 1 | 0 |
9 | 1 | 0 | 0 | 0 | 0 |
10 | 1 | 0 | 0 | 1 | 1 |
11 | 1 | 0 | 1 | 0 | 1 |
12 | 1 | 0 | 1 | 1 | 0 |
13 | 1 | 1 | 0 | 0 | 1 |
14 | 1 | 1 | 0 | 1 | 0 |
15 | 1 | 1 | 1 | 0 | 0 |
16 | 1 | 1 | 1 | 1 | 1 |
From the truth table the expression for the output parity checker bit is,
X (A, B, C, P) = Σ (0, 3, 5, 6, 9, 10, 12, 15)
K-Map for parity Checker:
The above expression is reduced as,
X = (A EXOR B EXOR C EXOR P)