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Task/Gray-code/00DESCRIPTION

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+[[wp:Gray code|Gray code]] is a form of binary encoding where transitions between consecutive numbers differ by only one bit. This is a useful encoding for reducing hardware data hazards with values that change rapidly and/or connect to slower hardware as inputs. It is also useful for generating inputs for [[wp:Karnaugh map|Karnaugh maps]] in order from left to right or top to bottom.
+
+Create functions to encode a number to and decode a number from Gray code. Display the normal binary representations, Gray code representations, and decoded Gray code values for all 5-bit binary numbers (0-31 inclusive, leading 0's not necessary).
+
+There are many possible Gray codes.  The following encodes what is called "binary reflected Gray code."
+
+Encoding (MSB is bit 0, b is binary, g is Gray code):
+<pre>if b[i-1] = 1
+   g[i] = not b[i]
+else
+   g[i] = b[i]</pre>
+Or:
+<pre>g = b xor (b logically right shifted 1 time)</pre>
+Decoding (MSB is bit 0, b is binary, g is Gray code):
+<pre>b[0] = g[0]
+
+for other bits:
+b[i] = g[i] xor b[i-1]</pre>
+
+;Reference
+* [http://www.wisc-online.com/Objects/ViewObject.aspx?ID=IAU8307 Converting Between Gray and Binary Codes]. It includes step-by-step animations.