Gray Code

Gray Code is a binary numeral system where 2 successive values differ in only one bit. It is also known as the reflected binary code

Given n-bit gray code it’s easy to write (n + 1)-bit gray code

1. Write down the 2-bit gray code (code in red)
2. Write down the reflected code (shown in green)
3. Put a ‘0’ at the beginning of each 2-bit Gray code and a ‘1’ at the beginning of each reflected code

Examples §

1-bit Gray Code §

0
1

2-bit Gray Code §

00
01
11
10

3-bit Gray Code §

000
001
011
010
110
111
101
100

Gray Code Simplification §

For n > 2, it is difficult to take advantage of the Gray code when the function is represented using the truth table. This is because input patterns that differ in only 1 position can be far apart in the truth table