Conversion from Gray Code to Binary Code and Vice Versa

Conversion from Gray Code to Binary Code

Let Gray Code be g₃  g₂  g₁  g₀. Then the respective Binary Code can be obtained as follows:

i.e.

b₃ = g₃

b₂ = b₃ ⊕ g₂

b₁ = b₂ ⊕ g₁

b₀ = b₁ ⊕ g₀
Example:

Gray Code: g₃  g₂  g₁  g₀  = 1 0 0 1  then Binary Code:  b₃  b₂  b₁  b₀

b₃ = g₃ = 1

b₂ = b₃ ⊕ g₂ = 1 ⊕ 0 = 1

b₁ = b₂ ⊕ g₁ = 1 ⊕ 0 = 1

b₀ = b₁ ⊕ g₀ =1 ⊕ 1 = 0

∴ Final Binary Code: 1 1 1 0

Conversion from Binary code to Gray Code

Let Binary code be b₃  b₂  b₁  b_0. Then the respective Gray Code can be obtained is as follows

i.e.

g₃ = b₃

g₂ = b₃ ⊕ b₂

g₁ = b₂ ⊕ b₁

g₀ = b₁ ⊕ b₀

 

Example:

Binary Code: b₃  b₂  b₁  b₀ = 1 1 1 0 Gray Code: g₃  g₂  g₁  g₀ 

g₃ = b₃ = 1

g₂ = b₃ ⊕ b₂ = 1 ⊕ 1 = 0

g₁ = b₂ ⊕ b₁ = 1 ⊕ 1 = 0

g₀ = b₁ ⊕ b₀ =1 ⊕ 0 = 1

∴ Final Gray code: 1 0 0 1

Conversion Table from Binary to Gray Code:

Decimal	Binary	Gray
0	0000	0000
1	0001	0001
2	0010	0011
3	0011	0010
4	0100	0110
5	0101	0111
6	0110	0101
7	0111	0100
8	1000	1100
9	1001	1101
10	1010	1111
11	1011	1110
12	1100	1010
13	1101	1011
14	1110	1001
15	1111	1000

Source:TESTBOOK