In reply to dave_59:
Yaa I agree with the XOR. As I stated earlier, I was not clear about the intent. This suggestion made it clear about distribution. Thanks for that.
I believed that first randomization will set any 3-4 bits out of 32 and the second/subsequent randomization will set some other bits. Thereby the previous bits will be reset and hence we can observe toggle of those bits. But this was a very rough idea. Your solution makes things clear.