79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
90 lines
3.4 KiB
Markdown
90 lines
3.4 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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---
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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">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">Karnaugh maps</a> in order from left to right or top to bottom.
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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."<br>Encoding (MSB is bit 0, b is binary, g is Gray code):
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<code><br>if b[i-1] = 1<br><span style="padding-left:1em">g[i] = not b[i]</span><br>else<br><span style="padding-left:1em">g[i] = b[i]</span><br>
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</code> Or: <br><code> g = b xor (b logically right shifted 1 time)</code><br>Decoding (MSB is bit 0, b is binary, g is Gray code): <br>
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<code>b[0] = g[0]<br>for other bits:<br>b[i] = g[i] xor b[i-1]<br></code>
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</section>
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## Instructions
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<section id='instructions'>
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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','<code>gray</code> should be a 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','<code>gray(true,177)</code> should return a 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,'<code>gray(true,177)</code> should return <code>233</code>.');
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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,'<code>gray(true,425)</code> should return <code>381</code>.');
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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,'<code>gray(true,870)</code> should return <code>725</code>.');
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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,'<code>gray(false,233)</code> should return <code>177</code>.');
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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,'<code>gray(false,381)</code> should return <code>425</code>.');
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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,'<code>gray(false,725)</code> should return <code>870</code>.');
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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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