Append a digit into an input HTML element via JavaScript function

I am creating a calculator and need to append numbers by clicking on a div button, instead of typing on the keyboard. But it must integrate with the use of the keyboard. Now, I know how to manipulate strings to achieve this, but positioning the blinking cursor at the end of the input element line escapes me...

Is there a way to call a keyboard event directly via a function call to emulate the key strokes, so that there is no manipulation of strings?

HTML input display markup...

    <div id="displayWindow" align="right">
        <input id="textInput" type="text" align-"right" value=""></input>
    </div>

And here is where I parse the incoming mouse event data:

function keyData(ev){
 var kee = ev.target.innerHTML;
 var nums = ".1234567890";
 if (nums.indexOf(kee)>=0){
    //Append value to number input display
    //  THIS IS WHERE I NEED HELP ....

 }
 var mathOps = "-+÷×±";
 if (mathOps.indexOf(kee)>=0){
    //Prepare math operations
 }
 var chars = "MC M+ M- MR";
 if (chars.indexOf(kee)>=0){
    //MEMORY handling functions
 }
 if (kee=="="){
    //Calculate
 }
 if (kee=="C"){
    //CLEAR everything
 }
}

Any help would be appreciated...

TIA

DK