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  • 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.

The previous video discussed about the BCD and X3 codes.

Subtitles and vocabulary

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B1 gray binary conversion error successive mirror

Introduction to Gray Code | GIntroduction to Gray Code | Gray to Binary code conversion | Binary to Gray code conversion | DE.07ray to Binary code conversion | Binary to Gray code conversion | DE.07

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    billy8077 posted on 2017/12/20
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