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Gray (ReflectedBinary or Mirror) Code
Gray code was invented by Frank Gray of Bell Labs in 1947. He called his code as reflected binary code. Later others started calling it as Gray code. This code has also come to be known as mirror code. Both the names, viz., reflected binary code and mirror code, stem from its mirrorreflection property. The main features of the Gray code are:
• It is a binary code just like to the conventional binary code.
• The code can be constructed using its mirrorreflecting property.
• Adjacent numbers of the code differ in one bitposition only. This is illustrated in Table 1.26, which shows entries of decimal numbers 0 to 4, and their equivalents in the conventional binary and the Graycode binary. In columns 2 and 3 of Table 1.26, we have highlighted the positions in which adjacent numbers differ from each other using bold fonts. It can be seen from column 2 that adjacent numbers in conventional binary may differ from each other in one or more one bit positions. For example, 0011 (= 3) and 0100 (= 4)differ from each other in three bit positions.
Now, inspection of column 3 of Table 1.26 shows that adjacent numbers in the Gray code differ from each other only in one bit position. For example, 0010 (= 3) and 0110 (= 4) differ from each other only in the second bit position from the left. This important property of Gray code has many practical applications. The foremost among these is its use in logic simplification using the Kmap and QuineMccluskey methods. It also finds extensive use in errordetection and correction codes.
Table 1.26 Decimal, conventional binary and Graycode numbers
The principles used in the construction of 2bit Gray code may be extended to get any nbit (where n is a power of 2) Gray code. Figure 1.5(a) and (b) show the construction of a 3bit Gray code. As in the 2bit case, in the case of 3bit Gray code, we shift the mirror to the new position below 10 and write the reflected code words below the mirror as shown in Fig. 1.5(a). After writing the reflected code words, as in the previous case, we add one 0 to each of the code words above the mirror one 1 to each of the code words below the mirror as shown in Fig. 1.5(b). Table 1.28 shows the actual form of the 3bit Gray code, after the removal of the mirror. Extending the principles, we draw the 4bit Gray code as shown in Table 1.29. it may be noted that Gray code is not a weighted code. But it finds applications because of its third feature (see Section 1.15).
• It is a binary code just like to the conventional binary code.
• The code can be constructed using its mirrorreflecting property.
• Adjacent numbers of the code differ in one bitposition only. This is illustrated in Table 1.26, which shows entries of decimal numbers 0 to 4, and their equivalents in the conventional binary and the Graycode binary. In columns 2 and 3 of Table 1.26, we have highlighted the positions in which adjacent numbers differ from each other using bold fonts. It can be seen from column 2 that adjacent numbers in conventional binary may differ from each other in one or more one bit positions. For example, 0011 (= 3) and 0100 (= 4)differ from each other in three bit positions.
Now, inspection of column 3 of Table 1.26 shows that adjacent numbers in the Gray code differ from each other only in one bit position. For example, 0010 (= 3) and 0110 (= 4) differ from each other only in the second bit position from the left. This important property of Gray code has many practical applications. The foremost among these is its use in logic simplification using the Kmap and QuineMccluskey methods. It also finds extensive use in errordetection and correction codes.
Table 1.26 Decimal, conventional binary and Graycode numbers
Decimal number

Conventional binary equivalent

Graycode equivalent

0
1
2
3
4

0000
0001
0010
0011
0100

0000
0001
0011
0010
0110

Construction of Gray code
Gray code can be constructed by its mirrorreflection property. For example, a twobit Gray code can be constructed as illustrated below. First we write 0 and then immediately below it write 1. Then we draw a horizontal line below bit 1 and then write the bits 1 and 0 below this line in that order, assuming the horizontal line to act as a mirror. Thus, we get the structure shown in Fig. 1.3.
Now, add one 0 each to the bits above the mirrorline and one 1 each to the bits below the mirrorline as demonstrated in Fig. 1.4. Table 1.27 shows the 2bit Gray code after removal of the mirror.
Table 1.28 3bit Gray code
Decimal

Gray code

0
1
2
3
4
5
6
7

000
001
011
010
110
111
101
100

Table 1.29 4bit Gray code
Decimal

Gray code

Decimal

Gray code

0
1
2
3
4
5
6
7

0000
0001
0011
0010
0110
0111
0101
0100

8
9
10
11
12
13
14
15

1000
1001
1011
1010
1110
1111
1101
1100

This post was written by: Sreejith Hrishikeshan
Sreejith Hrishikesan Nair is a MTech graduate in Communication Systems. He completed Btech Degree in Electronics and Communication.He is a person who wants to implement new ideas in the field of Technology.
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1 Responses to “Gray (ReflectedBinary or Mirror) Code”
26 November 2018 at 11:45
nice thank you
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