## 字幕列表 影片播放

• 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.

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# 灰色代碼簡介｜灰色代碼轉換｜二進制代碼轉換｜二進制代碼轉換｜DE.07ray到二進制代碼轉換｜二進制到灰色代碼轉換｜DE.07。 (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 conversio

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