freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/rosetta-code/gray-code.english.md

title, id, challengeType

title	id	challengeType
Gray code	5a23c84252665b21eecc7e80	5

Description

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 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):

if b[i-1] = 1
  g[i] = not b[i]
else
  g[i] = b[i]

Or:

g = b xor (b logically right shifted 1 time)

Decoding (MSB is bit 0, b is binary, g is Gray code):

b[0] = g[0]

for other bits:
b[i] = g[i] xor b[i-1]

Tests

tests:
  - text: <code>gray</code> should be a function.
    testString: assert(typeof gray=='function');
  - text: <code>gray(true,177)</code> should return a number.
    testString: assert(typeof gray(true,177)=='number');
  - text: <code>gray(true,177)</code> should return <code>233</code>.
    testString: assert.equal(gray(true,177),233);
  - text: <code>gray(true,425)</code> should return <code>381</code>.
    testString: assert.equal(gray(true,425),381);
  - text: <code>gray(true,870)</code> should return <code>725</code>.
    testString: assert.equal(gray(true,870),725);
  - text: <code>gray(false,233)</code> should return <code>177</code>.
    testString: assert.equal(gray(false,233),177);
  - text: <code>gray(false,381)</code> should return <code>425</code>.
    testString: assert.equal(gray(false,381),425);
  - text: <code>gray(false,725)</code> should return <code>870</code>.
    testString: assert.equal(gray(false,725),870);

Challenge Seed

function gray(enc, number) {
 // Good luck!
}

Solution

function gray(enc, number){
  if(enc){
      return number ^ (number >> 1);
  }else{
      let n = number;

      while (number >>= 1) {
          n ^= number;
      }
      return n;
  }
}