I've used following function for encoding binary data:
var base64_encode = function (data) {
    //  discuss at: http://phpjs.org/functions/base64_encode/
    // original by: Tyler Akins (http://rumkin.com)
    // improved by: Bayron Guevara
    // improved by: Thunder.m
    // improved by: Kevin van Zonneveld (http://kevin.vanzonneveld.net)
    // improved by: Kevin van Zonneveld (http://kevin.vanzonneveld.net)
    // improved by: Rafał Kukawski (http://kukawski.pl)
    // bugfixed by: Pellentesque Malesuada
    //   example 1: base64_encode('Kevin van Zonneveld');
    //   returns 1: 'S2V2aW4gdmFuIFpvbm5ldmVsZA=='
    //   example 2: base64_encode('a');
    //   returns 2: 'YQ=='
    var b64 = 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/=';
    var o1, o2, o3, h1, h2, h3, h4, bits, i = 0,
      ac = 0,
      enc = '',
      tmp_arr = [];
    if (!data) {
        return data;
    }
    do { // pack three octets into four hexets
        o1 = data.charCodeAt(i++);
        o2 = data.charCodeAt(i++);
        o3 = data.charCodeAt(i++);
        bits = o1 << 16 | o2 << 8 | o3;
        h1 = bits >> 18 & 0x3f;
        h2 = bits >> 12 & 0x3f;
        h3 = bits >> 6 & 0x3f;
        h4 = bits & 0x3f;
        // use hexets to index into b64, and append result to encoded string
        tmp_arr[ac++] = b64.charAt(h1) + b64.charAt(h2) + b64.charAt(h3) + b64.charAt(h4);
    } while (i < data.length);
    enc = tmp_arr.join('');
    var r = data.length % 3;
    return (r ? enc.slice(0, r - 3) : enc) + '==='.slice(r || 3);
}