Windoz 7 64-bit operating system has both IE8 32-bit and IE8 64-bit web browsers.
If you want to use the Java plugin with both of them you’ll need to download and install Java 32 bit and Java 64 bit !
To check if you are running 32bit or 64bit apps run task manager and look on the processes tab and you should see that 32bit apps have a “*32” appended to their image name.
Note there is currently only a 32bit version of the Adobe Flash Player plugin !
If you are interested in which version visitors to your webpage are using you can look at the http browser headers for the 32 bit browser
Mozilla/4.0 (compatible; MSIE 8.0; Windows NT 6.1; WOW64; Trident/4.0; SLCC2; .NET CLR 2.0.50727; .NET CLR 3.5.30729; .NET CLR 3.0.30729; Media Center PC 6.0; InfoPath.2; .NET4.0C; .NET4.0E)
and the 64 bit browser
Mozilla/4.0 (compatible; MSIE 8.0; Windows NT 6.1; Win64; x64; Trident/4.0; .NET CLR 2.0.50727; SLCC2; .NET CLR 3.5.30729; .NET CLR 3.0.30729; Media Center PC 6.0; .NET4.0C; .NET4.0E)