display an image,which is in base64 string format

You cannot fix IE8, right? :-)

Then you have two ways:

1. Fix your code the way supporting wider set of browser. If your implementation of the embedded base64 image is not incorrectly implemented (I have no idea how it could be incorrect as I cannot see your code), fix it. If it cannot be done, opt for the regular image file.
2. Reject some browsers you don't want to support. Say, if you detect that the browser is IE8, show a message recommending to upgrade this browser or use other browsers. You can find nice implementation of rejection, for example, here:
   http://jreject.turnwheel.com[^].

If you want to use approach #1, you may dislike the idea of a separate image file because you might be concerned with image hotlinking:
http://en.wikipedia.org/wiki/Inline_linking[^].

This would be a separate problem which has different solutions. For example, it can be done using ".htaccess" file or dynamic generation of the image content in HTTP response using one or another server-side technology. As I have no idea on what you have on server side, try to find the solution yourself, or ask some further question providing more information on your resources. Please see: http://bit.ly/1nk2tCA[^].

—SA