123 lines
2.4 KiB
Markdown
123 lines
2.4 KiB
Markdown
---
|
|
id: 5a23c84252665b21eecc7e80
|
|
title: Gray code
|
|
challengeType: 5
|
|
forumTopicId: 302276
|
|
dashedName: gray-code
|
|
---
|
|
|
|
# --description--
|
|
|
|
[Gray code](https://en.wikipedia.org/wiki/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 [Karnaugh maps](https://en.wikipedia.org/wiki/Karnaugh map) in order from left to right or top to bottom.
|
|
|
|
# --instructions--
|
|
|
|
Create a function to encode a number to and decode a number from Gray code. The function should will have 2 parameters.
|
|
|
|
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.
|
|
|
|
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]<br>
|
|
for other bits:
|
|
b[i] = g[i] xor b[i-1]
|
|
</pre>
|
|
|
|
# --hints--
|
|
|
|
`gray` should be a function.
|
|
|
|
```js
|
|
assert(typeof gray == 'function');
|
|
```
|
|
|
|
`gray(true,177)` should return a number.
|
|
|
|
```js
|
|
assert(typeof gray(true, 177) == 'number');
|
|
```
|
|
|
|
`gray(true,177)` should return `233`.
|
|
|
|
```js
|
|
assert.equal(gray(true, 177), 233);
|
|
```
|
|
|
|
`gray(true,425)` should return `381`.
|
|
|
|
```js
|
|
assert.equal(gray(true, 425), 381);
|
|
```
|
|
|
|
`gray(true,870)` should return `725`.
|
|
|
|
```js
|
|
assert.equal(gray(true, 870), 725);
|
|
```
|
|
|
|
`gray(false,233)` should return `177`.
|
|
|
|
```js
|
|
assert.equal(gray(false, 233), 177);
|
|
```
|
|
|
|
`gray(false,381)` should return `425`.
|
|
|
|
```js
|
|
assert.equal(gray(false, 381), 425);
|
|
```
|
|
|
|
`gray(false,725)` should return `870`.
|
|
|
|
```js
|
|
assert.equal(gray(false, 725), 870);
|
|
```
|
|
|
|
# --seed--
|
|
|
|
## --seed-contents--
|
|
|
|
```js
|
|
function gray(enc, number) {
|
|
|
|
}
|
|
```
|
|
|
|
# --solutions--
|
|
|
|
```js
|
|
function gray(enc, number){
|
|
if(enc){
|
|
return number ^ (number >> 1);
|
|
}else{
|
|
let n = number;
|
|
|
|
while (number >>= 1) {
|
|
n ^= number;
|
|
}
|
|
return n;
|
|
}
|
|
}
|
|
```
|