Conversion from Gray Code to Binary Code and Vice Versa

Conversion from Gray Code to Binary Code

Let Gray Code be g3  g 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  g 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  b0. 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  b= 1 1 1 0 Gray Code: g3  g2  g g

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

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