gray code to binary conversion

Bill Kingsley

Does anyone have some code for Gray code to binary conversion? I have a 12 bit rotary encoder that outputs gray code in parallel. I input this to 2 74HC165 shift registers then serialy load to the BS2 in a 16 bit word variable. I need a routine to convert the 16 bit Gray code to binary.

Thanks,

Bill

Bruce Bates

Bill -

Sorry, I don't have a code snippet handy, but here is the method:
http://www.shef.ac.uk/physics/teaching/phy107/solvegray.html

I suspect the resident math guru, Dr. Tracy Allen, may have a simple answer for you as soon as he sees your question.

Regards,

Bruce Bates

Jon Williams

After a bit of web research I found a simple description of the conversion here: http://cafaq.com/extra/gray.html

With that I wrote the attached program.· It works with 4-bit variables, and can easily be modified to work with your data.

Update: After looking at the URL Bruce provided, I updated my program a bit to follow that algorithm (uses + instead of ^).· The result is the same and expect it will work·a bit faster for large values.·

Updated again with Tracy's Binary to Gray technique that doesn't require a loop.


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Jon Williams
Applications Engineer, Parallax
Dallas Office

Post Edited (Jon Williams) : 12/18/2004 2:21:40 PM GMT

Bill Kingsley

Bruce, I did not have time to look at URL yet...Just wanted to say thanks and that I can remember Tracy from years ago on the old Parallax forum...Its been a long time since I "unsubscribed" due to 50 to 100 emails a day. This new format is so much better!

Tracy Allen

Hi Bill,

Good to see you around again! I do have bit of a writeup at this URL: www.emesystems.com/BS2fsm.htm#Gray%20code
It is essentially the same as Jon's program.

A 16 bit code follows the same pattern:

bn.bit15=gc.bit15  ' convert to binary from Gray
for idx=14 to 0    ' bit by bit XOR
   bn.bit0(idx)=bn.bit0(idx+1)^gc.bit0(idx)
 next

You might want to take a look at Art of Electronics, as there is a cute circuit there using XOR gates and a funny story.

The conversion from binary to Gray code is much easier, and does not require a loop, just XOR the binary word with itself, shifted one right:
graycode=(binary>>1) ^ binary

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Tracy Allen
www.emesystems.com

Bill Kingsley

Thanks Jon and Tracy, I will try this as soon a I have a little time. It evaporates quickly this time of year!

Bill Kingsley

Hi guys, I tried Tracy's code today..works great. I had to invert the data from the encoder since its outputs are active low. I then modified the iterations of idx from 15 to 9 since my encoder is 10 bit. I have not tried Jon's code yet to see which is faster, however for this app. speed is so-not an issue. We are positioning a reflector a few times per hour in relation to the Sun. We will use astronomical data and a Dallas DS1302 RTC to predict the correct position.

Jon Williams

Since there's lots of internal bit indexing, the difference speed difference will probably be negligible. When using bits though (where carries are discarded), it turns out that addition and XOR work the same

0 ^ 0 = 0 ... 0 + 0 = 0
0 ^ 1 = 1 ... 0 + 1 = 1
1 ^ 0 = 1 ... 1 + 0 = 1
1 ^ 1 = 0 ... 1 + 1 = 0 (bit that carried is lost)

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Jon Williams
Applications Engineer, Parallax
Dallas Office

Tracy Allen

Yes, the hardware implementation of a half adder uses an XOR gate and an AND gate.

There is a carry from the sum of two bits only when both bits are one.

A full adder allows the sum of three bits (one of which is usually the carry from the previous column). The sum bit is simply the XOR of all three, and there is a carry if any two bits are ones. The maximum value is of course %1+%1+%1 = %11
SUM1 = A1 XOR B1 XOR Carry0
Carry1 = (A1 AND Carry0) OR (B1 AND Carry0) OR (A1 AND B1)
The full adder in hardware takes two half adders, one more XOR, one more AND and one three-input OR gate.

The circuit in Art of Electronics shows how to implement both the Gray->binary and binary->Gray conversions using only XOR gates. Those are static logic circuits (except for propation delays), but I don't see how to do it without a loop on the Stamp. The FOR-NEXT structure is slow on the Stamp--so you could simply repeat the code for each bit. Jon also pointed out to that the index logic is slow. Something using shifts and mask logic might be faster, but, you don't need it, so why push it?

Jon Williams said...
Since there's lots of internal bit indexing, the difference speed difference will probably be negligible. When using bits though (where carries are discarded), it turns out that addition and XOR work the same

0 ^ 0 = 0 ... 0 + 0 = 0
0 ^ 1 = 1 ... 0 + 1 = 1
1 ^ 0 = 1 ... 1 + 0 = 1
1 ^ 1 = 0 ... 1 + 1 = 0 (bit that carried is lost)

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Tracy Allen
www.emesystems.com