JavaScript (ES6), 78 74 bytes
f=(n,i)=>n<999.5?i?n.toPrecision(n<1^3)+' KMG'[i]+'iB':n+'B':f(n/1024,-~i)
<input oninput=o.textContent=f(this.value)><pre id=o>
Edit: Saved 4 bytes thanks to @Arnauld.
f=(n,i)=>n<999.5?i?n.toPrecision(n<1^3)+' KMG'[i]+'iB':n+'B':f(n/1024,-~i)
<input oninput=o.textContent=f(this.value)><pre id=o>
Edit: Saved 4 bytes thanks to @Arnauld.