I have a C++ console application (exe) that connects to a server and writes dynamic data to the console, how could I push that dynamic data to a web application in real time using node.js.
You could start the C++ application as a child process within your Node.js server code. I don't know what (if any) framework you're using, but in a framework like Express.js this is easy enough to do in your route logic.
You'll want to take a look at the child_process documentation for node, which can be found here http://nodejs.org/api/child_process.html.
var exec = require('child_process').exec
var _process = exec('command to invoke binary');
_process.stdout.on('data',function(data){
console.log(data);
});
This code includes the child_process module, and then executes the command needed to invoke your C++ binary. Then, it waits and logs any data this process prints to stdout to the console. Instead of printing out to the console, you can include this code within an HTTP server, and can then send it back as part of response data.