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Last updated: 29-01-09

Frank Gray got in 1947 a patent at his - reflected binary code - known as the Gray code - Read more in this Wikipedia link

Wheel with 3-bit Gray code

What's special for a Gray code compared with a Binary code?

Answer:   Only one bit changes between a given gray code and its neighbour codes

Wheel with 3-bit Binary code

What could course the problems, using a binary coded wheel?

Answer:  The wheel must of course be very precise - specially when more the one but should change 0->1 or 1->0.
But also the decoders must be very similar (same characteristic) and must be situated precisely @ a strait line.

Digital "circuit" for Binary to Gray code conversion

Given a 8-bit Binary code = 1 0 1 0 1 1 0 1   how would the corresponding  gray code look like?

Answer:  1 0 1 0 1 1 0 1
0 1 0 1 0 1 1 0
--------------------- XOR

1 1 1 1 1 0 1 1

Digital "circuit" for Gray to Binary code conversion (may be ... please verify yourself)

Answer:   Fill out the Carnaugh maps below and find the equations for a Gray to Binary converter
For a solution - drag the mouse over the maps below while holding the left button

 gray Q2Q1 Q0 00 01 11 10 0 0 0 1 1 1 0 0 1 1 Binary Q2= gray Q2

 gray Q2Q1 Q0 00 01 11 10 0 0 1 0 1 1 0 1 0 1 Binary Q1= Q2 xor Q1

 gray Q2Q1 Q0 00 01 11 10 0 0 1 0 1 1 1 0 1 0 Binary Q0= Q2 xor Q1xor Q0

Given a 8-bit Gray code = 1 1 1 1 1 0 1 1 how would the corresponding  binary code look like? - test the algorithm from above

Gray code

 1 1 1 1 1 0 1 1 xor : : : : : : 0 xor : : : : : 1 xor : : : : 0 xor : : : 1 xor : : 1 xor : v v v v v v 0 xor 1 0 1 0 1 1 0 1
Binary code