Gray Code

The gray code is a binary numeral system there two successive values differ by only one bit. It is also known as the reflected binary code.

1-bit gray code: 0 and 1

2-bit gray code:

Decimal Gray Code
0 00
1 01
2 11
3 10

3-bit gray code:

Decimal Gray Code
0 000
1 001
2 011
3 010
4 110
5 111
6 101
7 100

Gray Code Simplification

Example

Find the simplest function for the truth table:
0 0 1
0 1 1
1 0 0
1 1 1

solution
Canonical SOP:

(see partial distributive law)

However, we can rearrange the table:
0 0 1
0 1 1
1 1 1
1 0 0

Which makes Gray code on the and columns.

Taking the first two columns, we have (that is, the result is true for ), and the second and third columns give , so the function is represented as