Binary-to-Gray code Conversion
Conversion between binary code and Gray code is sometimes useful. The
following rules explain how to convert from a binary number to a Gray code
word:
1. The most significant bit (left-most) in the Gray code is the same as the
corresponding MSB in the binary number.
2. Going from left to right, add each adjacent pair of binary code bits to
get the next Gray code bit. Discard carries.
For example, the conversion of the binary number 10110 to Gray code is as
follows:
1
+
0
+
1
+
1
+
0 Binary
1 1 1 0 1 Gray
The Gray code is 1 1 101.
Gray -to- Binary Conversion
To convert from Gray code to binary, use a similar method; however, there
are some differences. The following rules apply:
1. The most significant bit (left-most) in the binary code is the same as
the corresponding bit in the Gray code.
2. Add each binary code bit generated to the Gray code bit in the next
adjacent position. Discard carries.
For example, the conversion of the Gray code word 11011 to binary is as
follows:
1 1 0 1 1 Gray
+
+
+
+
1 0 0 1 0 Binary
The binary number is 10010.
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