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Digital Electronics
Table 2.5 Generation of a larger word-length ternary Gray code.
One-digit ternary code
Two-digit ternary code
Three-digit ternary code
0
0
00
00
000
1
1
01
01
001
2
2
02
02
002
2
1 2
1 2
0 1 2
1
1 1
1 1
0 1 1
0
1 0
1 0
0 1 0
0
2 0
2 0
0 2 0
1
2 1
2 1
0 2 1
2
2 2
2 2
0 2 2
22
122
21
121
20
120
10
110
11
111
12
112
02
102
01
101
00
100
00
200
01
201
02
202
12
212
11
211
10
210
20
220
21
221
22
222
angle is represented in straight binary. The cyclic property of the Gray code is a plus in this
application.
3. The Gray code is used for labelling the axes of Karnaugh maps, a graphical technique used for
minimization of Boolean expressions.
4. The use of Gray codes to address program memory in computers minimizes power consumption.
This is due to fewer address lines changing state with advances in the program counter.
5. Gray codes are also very useful in genetic algorithms since mutations in the code allow for mostly
incremental changes. However, occasionally a one-bit change can result in a big leap, thus leading
to new properties.
Example 2.4
Find (a) the Gray code equivalent of decimal 13 and (b) the binary equivalent of Gray code number
1111.