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Binary and Gray Code

The output data of many physical systems are quantities that are continuous. These data must be converted into digital form before they are applied to a digital system. Continuous or analog information is converted into digital form by means of an analog-to-digital converter. It is sometimes convenient to use the Gray code shown in Table 1 to represent digital data that have been converted from analog data. The advantage of the Gray code over the straight binary number sequence is that only we bit in the code group changes in going from one number to the next. For example, in going from 7 to 8, the Gray code changes from 0100 to 1100. My the first bit changes, from 0 to 1: the other three bits remain the same. By contrast, with binary numbers the change from 7 to 8 will be from 0111 to 1000, which causes all four bits to change values.

Table 1.

Figure 1 and 2 below are the idea for conversion of binary to gray code and the opposite by using EX-OR gate.

Figure 1. Binary to Gray Code Conversion.

Figure 2. Gray Code to Binary.

　Source: Digital Design, M.Morris Mano

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