Binary - Gray Code Conversion with Solved Examples

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It's easy to calculate the Gray code for any integer, j: We can express this in Scheme as. Going from a Gray Code back to its binary equivalent is a little harder. Gray codes are useful in situations where analog information is being converted to digital information or vice versa. It often happens that there are ambiguities where, say, an analog value changes from one value to the next. At the sector boundaries it's unclear what the correct values are and encoding them in the normal binary encoding can lead to large errors.

With the Gray coding, the errors are always localized to one bit so that the values are never more than one off. That explanation is a little hard to follow without Knuth's diagram and is, in any event, not a real application although one can imagine the same basic scheme being used in one. Mark Dominus over at The Universe of Discourse has a nice post from that shows a perfect real-world application of Use of binary to gray code conversion codes.

It's a stadiometera device used in medical settings to measure a person's height. Commonly they are attached to a scale and consist of a slider that can be moved up and down a column marked with the heights and a piece that sticks out and rests on the top of the patient's head.

We've all been measured by one of these and usually the doctor or nurse just reads off the number from the column. In Dominus' example, the stadiometer was digital and worked by a photosensor reading a pattern from the column. That pattern turns out to be a Gray code and, as Dominus illustrates, is used precisely to avoid measurement errors when the slider is between two possible height values.

Follow the link use of binary to gray code conversion see a picture of the column with its Gray codes and a worked example of how large the measurement error can be if normal binary encoding were used. The one given here is the one specified by Gray. The minds had long ago come up with a proper name for it; they called it the Irreal, but they thought of it as Infinite Fun.

That was what they really knew it as. The Land of Infinite Fun. This entry was posted in General and tagged Scheme. Use of binary to gray code conversion powered by WordPress.

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