|
|
| |
|
Last updated:
13-07-09 |
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 |
|
|
|
|
|
|
 |
