The previous video discussed about the BCD and X3 codes.
U can check the links in the description to check that video.
In this video we will talk about the gray code, its applications and the conversion
from gray to binary and binary to gray.
This code is also known as the reflective code because of its peculiar arrangement or
representation.
This code is named after Frank Gray and the successive numbers differ only by the single
bit.
Let us take a look at how to construct this code.
If it consists of only one bit we can represent two numbers i.e) 0 and 1.
On adding one more bit, 4 numbers can be represented.
To write the numbers in ascending order using Gray code, we use something called mirror
technique.
Let us try it to write the numbers 0 to 3.
0 is represented as 00 and 1 as 01.
Now the next two digits are obtained by changing MSB from 0 to 1 and placing a mirror at LSB.
This will give us 11 for 2 and 10 for 3.
If we look at the numbers, we can see that each successive number is different from the
previous bit by only one bit.
By adding one more bit, that is three bits altogether, we can represent 8 numbers.
Let us try the mirroring technique.
Every time the bits end, add 1 as MSB and place mirror below the remaining bits to get
its reflection and one gets the decimal numbers
So now we understand why it is called as reflective code.
This code was developed as error checking code.
As each successive numbers differ only by a single bit, this code finds use in error
checking and corrections in digital communications.
Now let us try converting binary numbers to Gray code.
For this we must know the XOR operation which has been covered in the other lecture of this
series.
You can find the link to that video in the description below or the suggested card in
the top right corner of the video.
The MSB of gray code will be same as MSB of binary.
The next lower bit of gray code is obtained by taking X-or of MSB and next lower
bit of binary number.
The process of XORing continues till all the binary bits are converted to gray code.
Let us try with an example.
We will convert 1010 to gray code.
The MSB 1 is copied as it is to give MSB of gray code.
Next bit of Gray code is obtained by taking X-OR of 1 and 0 which gives 1, X-ORing 0 and
1 gives 1 and X-ORing 1 and 0 gives 1.
So the obtained gray code is 1111.
We continue with understanding gray to binary conversion.
The MSB of gray is copied as it is to give MSB of binary.
The next binary bits are obtained by X-ORing the existing binary bit with GRAY bits.
We will convert 1010 from GRAY to binary.
The MSB will be 1.
Now we will X-OR the MSB of binary with the next lower bit of GRAY
X-ORing 1 and 0 will produce 1.
This 1 on X-ORing with 1 will give 0 and X-ORing 0 with 0 will produce 0.
So the binary equivalent is 1100 for GRAY code 1010.
The next video in this series will discuss the error detection techniques and error detection
codes.