Eg. Now form a hamming code for 5-bit information bits 10110 with odd parity m=5 and we have to follow 2p >= m + p + 1 The value of p as 4 to satisfy 24 (16) >= 5 + 4 + 1 but p=3 doesn’t satisfy as 23 (8) >= 5 + 3 + 1 So […]

# Binary Code

## Example 1: Hamming code & parity bit

Eg. So let’s form hamming code using 4-bit message bits 1101 with parity bits as even parity bit and check how it is able to detect and correct error. As we have already decided parity bit positions and their corresponding message bits for a 4-bit message For the moment we have hamming code as P1 P2 1 P3 1 […]

## Parity bit relation with message bits

E.g. Consider the parity bit P1 and we have to find the position of message bits which we’ll cover with this parity bit. Firstly write the binary equivalents of positions of message bit Bit1 bit2 bit3 bit4 bit5 bit6 bit7 Parity parity parity P1 P2 M1 P3 M2 M3 M4 001 010 011 […]

## Hamming code

This code is used for single error correction i.e. using this code we can detect only single error. In parity bit method we used only single extra bit but in this method number of extra bits (which also are parity bits) vary with the number of bits of the message. Suppose we have the number […]

## Parity Bit questions

Q1. Find out the parity bit (odd) for message 1100 As 1100 has 2 i.e. even number of 1’s so we take parity bit (odd) as 1 to make odd number of 1’s out of 5 bits So message we send is 11001 (5th is the parity bit) Q2. Find out the parity bit (even) for […]

## Error detection by Parity bit

Eg. Find out the parity bit (odd) for message 1101 and show us how it helps in detecting errors As 1101 has 3 i.e. odd number of 1’s so P=0 so that we still have the odd number of 1’s in the combination of 5 bits(message(4 bits) and parity bit(1 bit)) So message we send […]

## Parity bit

A parity bit is an extra bit that is attached to the information that is being sent from one position to the other. This bit is attached just to detect the error if any in the information during the transmission. This bit is used to make number of 1’s in the message or information either […]

## M out of N coding scheme And its efficiency

In this coding scheme we have N total number of bits and fixed M of those bits are 1s and N – M bits are 0s. Hence this scheme is called M out of N coding scheme. It is a type of Error-Detecting coding scheme as if during transmission we have any error in the message we […]

## Gray Code

This is also called unit distance code or reflected code. This coding system has a property that there is only one bit change between consecutive gray codes. The following table would show gray codes of decimal values. Binary to gray conversion: Starting from right to left If it is MSB then place it as it is […]

## Excess-3 Code

It is also known as XS-3. We add 310 or 1102 to the each 4-bit combination of BCD codes to get excess-3 codes. We can see the corresponding Excess-3 codes of each BCD number: Decimal Binary BCD Excess-3 0 0000 0000 0011 0001 0001 0100 0010 0010 0101 0011 0011 0110 0100 0100 0111 0101 […]