104 lines
2.9 KiB
Markdown
104 lines
2.9 KiB
Markdown
---
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title: Gray code
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id: 5a23c84252665b21eecc7e80
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challengeType: 5
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forumTopicId: 302276
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---
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## Description
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<section id='description'>
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<a href="https://en.wikipedia.org/wiki/Gray code" target="_blank">Gray code</a> is a form of binary encoding where transitions between consecutive numbers differ by only one bit.
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This is a useful encoding for reducing hardware data hazards with values that change rapidly and/or connect to slower hardware as inputs.
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It is also useful for generating inputs for <a href="https://en.wikipedia.org/wiki/Karnaugh map" target="_blank">Karnaugh maps</a> in order from left to right or top to bottom.
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</section>
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## Instructions
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<section id='instructions'>
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Create a function to encode a number to and decode a number from Gray code. The function should will have 2 parameters.
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The first would be a boolean. The function should encode for true and decode for false. The second parameter would be the number to be encoded/decoded.
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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>
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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]
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</pre>
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Or:
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<pre>
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g = b xor (b logically right shifted 1 time)
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</pre>
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Decoding (MSB is bit 0, b is binary, g is Gray code):
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<pre>
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b[0] = g[0]<br>
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for other bits:
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b[i] = g[i] xor b[i-1]
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</pre>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>gray</code> should be a function.
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testString: assert(typeof gray=='function');
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- text: <code>gray(true,177)</code> should return a number.
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testString: assert(typeof gray(true,177)=='number');
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- text: <code>gray(true,177)</code> should return <code>233</code>.
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testString: assert.equal(gray(true,177),233);
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- text: <code>gray(true,425)</code> should return <code>381</code>.
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testString: assert.equal(gray(true,425),381);
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- text: <code>gray(true,870)</code> should return <code>725</code>.
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testString: assert.equal(gray(true,870),725);
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- text: <code>gray(false,233)</code> should return <code>177</code>.
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testString: assert.equal(gray(false,233),177);
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- text: <code>gray(false,381)</code> should return <code>425</code>.
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testString: assert.equal(gray(false,381),425);
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- text: <code>gray(false,725)</code> should return <code>870</code>.
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testString: assert.equal(gray(false,725),870);
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function gray(enc, number) {
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// Good luck!
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}
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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function gray(enc, number){
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if(enc){
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return number ^ (number >> 1);
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}else{
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let n = number;
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while (number >>= 1) {
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n ^= number;
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}
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return n;
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}
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}
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```
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</section>
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