Binary Gray code conversion

grayBin.js

function reverse(array) {
  var copy = array.slice();
  copy.reverse();
  return copy;
}

function gray(nbits) {
  if (nbits <= 0) return ['']; // zero bit code contains 2^0 values == 1
  
  var gray0 = gray(nbits - 1);
  
  var lower = gray0.map(function(b) { return '0' + b; });
  var upper = reverse(gray0).map(function(b) {
    return '1' + b;
  });
  
  return lower.concat(upper);
}


function not(bits) {
  return bits.split('').
    map(function(c) { return c == '0' ? '1' : '0'; }).
    join('')
}

function shiftR(bits) {
  return '0' + bits.substring(0, bits.length-1);
}

function xor(a, b) {
  var sum = [];
  
  for (var i = 0; i < a.length; i++) {
    sum[i] = ((a[i] == '1') ^ (b[i] == '1')) ? '1' : '0';
  }
  
  return sum.join('');
}

function gray2bin(g) {
  if (g === '') return ''; // zero bit code
  
  var firstBit = g.charAt(0);
  if (firstBit == '0') {
    return '0' + gray2bin(g.substring(1))
  }
  else {
    return '1' + not(gray2bin(g.substring(1)))
  }
}

function bin2gray(b) {
  if (b === '') return ''; // zero bit code
  
  var firstBit = b.charAt(0);
  if (firstBit == '0') {
    return '0' + bin2gray(b.substring(1));
  }
  else {
    return '1' + bin2gray(not(b.substring(1)));
  }
}

function bin2grayFast(b) {
  return xor(b, shiftR(b));
}

function toBinary(n) {
  return n.toString(2)
}

function padLeftSlow(s, padding, totalLength) {
  // not efficient
  while (s.length < totalLength) {
    s = padding + s;
  }
  
  return s;
}

function printGray(grayCode) {
  var columnWidth = 15;
  var nbits = grayCode[0].length;
  
  function col(s) { return padLeftSlow(s, ' ', columnWidth); }
  
  console.log(col('INDEX') + '|' +
              col('GRAY') + '|' +
              col('BIN2GRAY') + '|' +
              col('BIN2GRAY FAST'));
  
  for (var i = 0; i < grayCode.length; i++) {
    var indexStr = padLeftSlow(toBinary(i), '0', nbits);
    var grayStr = grayCode[i];
    var gray2Str = bin2gray(indexStr);
    var gray3Str = bin2grayFast(indexStr);
    
    console.log(col(indexStr) + '|' + 
                col(grayStr) + '|' +
                col(gray2Str) + '|' +
                col(gray3Str));
  }
}


printGray(gray(3));
printGray(gray(4));