Saving binary data as file using JavaScript from a browser

Question 1

This is possible if the browser supports the download property in anchor elements.

var sampleBytes = new Int8Array(4096);

var saveByteArray = (function () {
    var a = document.createElement("a");
    document.body.appendChild(a);
    a.style = "display: none";
    return function (data, name) {
        var blob = new Blob(data, {type: "octet/stream"}),
            url = window.URL.createObjectURL(blob);
        a.href = url;
        a.download = name;
        a.click();
        window.URL.revokeObjectURL(url);
    };
}());

saveByteArray([sampleBytes], 'example.txt');

JSFiddle: http://jsfiddle.net/VB59f/2

Question 2

Use FileSaver.js. It supports Chrome, Edge, Firefox, and IE 10+ (and probably IE < 10 with a few "polyfills" - see Note 4). FileSaver.js implements the saveAs() FileSaver interface in browsers that do not natively support it:
https://github.com/eligrey/FileSaver.js

Minified version is really small at < 2.5KB, gzipped < 1.2KB.

Usage:

/* TODO: replace the blob content with your byte[] */
var blob = new Blob([yourBinaryDataAsAnArrayOrAsAString], {type: "application/octet-stream"});
var fileName = "myFileName.myExtension";
saveAs(blob, fileName);

You might need Blob.js in some browsers (see Note 3). Blob.js implements the W3C Blob interface in browsers that do not natively support it. It is a cross-browser implementation:
https://github.com/eligrey/Blob.js

Consider StreamSaver.js if you have files larger than blob's size limitations.

Complete example:

/* Two options
 * 1. Get FileSaver.js from here
 *     https://github.com/eligrey/FileSaver.js/blob/master/FileSaver.min.js -->
 *     <script src="FileSaver.min.js" />
 *
 * Or
 *
 * 2. If you want to support only modern browsers like Chrome, Edge, Firefox, etc., 
 *    then a simple implementation of saveAs function can be:
 */
function saveAs(blob, fileName) {
    var url = window.URL.createObjectURL(blob);

    var anchorElem = document.createElement("a");
    anchorElem.style = "display: none";
    anchorElem.href = url;
    anchorElem.download = fileName;

    document.body.appendChild(anchorElem);
    anchorElem.click();

    document.body.removeChild(anchorElem);

    // On Edge, revokeObjectURL should be called only after
    // a.click() has completed, atleast on EdgeHTML 15.15048
    setTimeout(function() {
        window.URL.revokeObjectURL(url);
    }, 1000);
}

(function() {
    // convert base64 string to byte array
    var byteCharacters = atob("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");
    var byteNumbers = new Array(byteCharacters.length);
    for (var i = 0; i < byteCharacters.length; i++) {
        byteNumbers[i] = byteCharacters.charCodeAt(i);
    }
    var byteArray = new Uint8Array(byteNumbers);
    
    // now that we have the byte array, construct the blob from it
    var blob1 = new Blob([byteArray], {type: "application/octet-stream"});

    var fileName1 = "cool.gif";
    saveAs(blob1, fileName1);

    // saving text file
    var blob2 = new Blob(["cool"], {type: "text/plain"});
    var fileName2 = "cool.txt";
    saveAs(blob2, fileName2);
})();

JSFiddle here: should download two small files when the page loads - a binary file (GIF) and a text file. Update: StackOverflow's Run code snippet doesn't support downloading files anymore as sandboxes by default don't allow downloading files in newer browser versions.)

Tested on Chrome, Edge, Firefox, and IE 11 (use FileSaver.js for supporting IE 11).
You can also save from a canvas element. See https://github.com/eligrey/FileSaver.js#saving-a-canvas.

Demos: https://eligrey.com/demos/FileSaver.js/

Blog post by author of FileSaver.js: http://eligrey.com/blog/post/saving-generated-files-on-the-client-side

Note 1: Browser support: https://github.com/eligrey/FileSaver.js#supported-browsers

Note 2: Failed to execute 'atob' on 'Window'

Note 3: Polyfill for browsers not supporting Blob: https://github.com/eligrey/Blob.js
See http://caniuse.com/#search=blob

Note 4: IE < 10 support (I've not tested this part):
https://github.com/eligrey/FileSaver.js#ie--10
https://github.com/eligrey/FileSaver.js/issues/56#issuecomment-30917476

Downloadify is a Flash-based polyfill for supporting IE6-9: https://github.com/dcneiner/downloadify (I don't recommend Flash-based solutions in general, though.)
Demo using Downloadify and FileSaver.js for supporting IE6-9 also: http://sheetjs.com/demos/table.html

Note 5: Creating a BLOB from a Base64 string in JavaScript

Note 6: FileSaver.js examples: https://github.com/eligrey/FileSaver.js#examples

Question 3

Try

let bytes = [65,108,105,99,101,39,115,32,65,100,118,101,110,116,117,114,101];

let base64data = btoa(String.fromCharCode.apply(null, bytes));

let a = document.createElement('a');
a.href = 'data:;base64,' + base64data;
a.download = 'binFile.txt'; 
a.click();

I convert here binary data to base64 (for bigger data conversion use this) - during downloading browser decode it automatically and save raw data in file. 2020.06.14 I upgrade Chrome to 83.0 and above SO snippet stop working (probably due to sandbox security restrictions) - but JSFiddle version works - here

Question 4

To do this task download.js library can be used. Here is an example from library docs:

download("data:image/gif;base64,R0lGODlhRgAVAIcAAOfn5+/v7/f39////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////yH5BAAAAP8ALAAAAABGABUAAAj/AAEIHAgggMGDCAkSRMgwgEKBDRM+LBjRoEKDAjJq1GhxIMaNGzt6DAAypMORJTmeLKhxgMuXKiGSzPgSZsaVMwXUdBmTYsudKjHuBCoAIc2hMBnqRMqz6MGjTJ0KZcrz5EyqA276xJrVKlSkWqdGLQpxKVWyW8+iJcl1LVu1XttafTs2Lla3ZqNavAo37dm9X4eGFQtWKt+6T+8aDkxUqWKjeQUvfvw0MtHJcCtTJiwZsmLMiD9uplvY82jLNW9qzsy58WrWpDu/Lp0YNmPXrVMvRm3T6GneSX3bBt5VeOjDemfLFv1XOW7kncvKdZi7t/S7e2M3LkscLcvH3LF7HwSuVeZtjuPPe2d+GefPrD1RpnS6MGdJkebn4/+oMSAAOw==", "dlDataUrlBin.gif", "image/gif");