Digital Electronics: Principles, Devices and Applications

26 Digital ElectronicsTable 2.5Generation of a larger word-length ternary Gray code.One-digit ternary code Two-digit ternary code Three-digit ternary code0 0 00 00 0001 1 01 01 0012 2 02 02 0022 12 12 0121 11 11 0110 10 10 0100 20 20 0201 21 21 0212 22 22 02222 12221 12120 12010 11011 11112 11202 10201 10100 10000 20001 20102 20212 21211 21110 21020 22021 22122 222angle is represented in straight binary. The cyclic property of the Gray code is a plus in thisapplication.3. The Gray code is used for labelling the axes of Karnaugh maps, a graphical technique used forminimization 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 mostlyincremental changes. However, occasionally a one-bit change can result in a big leap, thus leadingto new properties.Example 2.4Find (a) the Gray code equivalent of decimal 13 and (b) the binary equivalent of Gray code number1111.