29 lines
1.2 KiB
Plaintext
29 lines
1.2 KiB
Plaintext
[[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.
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Create functions to encode a number to and decode a number from Gray code.
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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).
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There are many possible Gray codes. The following encodes what is called "binary reflected Gray code."
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Encoding (MSB is bit 0, b is binary, g is Gray code):
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<pre>if b[i-1] = 1
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g[i] = not b[i]
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else
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g[i] = b[i]</pre>
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Or:
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<pre>g = b xor (b logically right shifted 1 time)</pre>
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Decoding (MSB is bit 0, b is binary, g is Gray code):
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<pre>b[0] = g[0]
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for other bits:
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b[i] = g[i] xor b[i-1]</pre>
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;Reference
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* [http://www.wisc-online.com/Objects/ViewObject.aspx?ID=IAU8307 Converting Between Gray and Binary Codes]. It includes step-by-step animations.
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