1. Gray Code Converters
Discussion D9.1
Example 16

2. Gray Code Definition: An ordering of 2n binary numbers such that
only one bit changes from one entry to the next.
Binary coding {0...7}: {000, 001, 010, 011, 100, 101, 110, 111}
Gray coding {0...7}: {000, 001, 011, 010, 110, 111, 101, 100}
Not unique
One method for generating a Gray code sequence:
Start with all bits zero and successively flip the right-most bit that produces a new string.

3. Binary - Gray Code Conversions
Gray code: G(i), i = n – 1 downto 0
Binary code: B(i), i = n – 1 downto 0
Binary coding {0...7}: {000, 001, 010, 011, 100, 101, 110, 111}
Gray coding {0...7}: {000, 001, 011, 010, 110, 111, 101, 100}
Convert Binary to Gray:
Copy the most significant bit.
For each smaller i
G(i) = B(i+1) xor B(i)
Convert Gray to Binary:
Copy the most significant bit.
For each smaller i
B(i) = B(i+1) xor G(i)

4. bin2gray.vhd library IEEE; use IEEE.STD_LOGIC_1164.all;
entity bin2gray is
generic(width:positive := 3);
port(
b : in STD_LOGIC_VECTOR(width-1 downto 0);
g : out STD_LOGIC_VECTOR(width-1 downto 0) );
end bin2gray;
architecture bin2gray of bin2gray is
begin
process(b)
g(width-1) <= b(width-1);
for i in width-2 downto 0 loop
g(i) <= b(i+1) xor b(i);
end loop;
end process;

5. Binary to Gray Code Conversion

6. gray2bin.vhd library IEEE; use IEEE.STD_LOGIC_1164.all;
entity gray2bin is
generic(width:positive := 3);
port(
g : in STD_LOGIC_VECTOR(width-1 downto 0);
b : out STD_LOGIC_VECTOR(width-1 downto 0) );
end gray2bin;
architecture gray2bin of gray2bin is
begin
process(g)
variable bv: STD_LOGIC_VECTOR(width-1 downto 0);
bv(width-1) := G(width-1);
for i in width-2 downto 0 loop
bv(i) := bv(i+1) xor g(i);
end loop;
b <= bv;
end process;
gray2bin.vhd

7. Gray Code to Binary Conversion