 0 460

## 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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