Anyone suggest which IC can be used for converting 5 V / 3 V to 0.5 V?
and also which IC can be used for converting 0.5 V to 5 V/ 3 V?

 

to 0.5 V

Tell us more about "0.5V".
The 5V/3V is probably TTL/CMOS logic.
How fast? mS or uS or nS?

 

I am feeding 0.5 V to HMC726LC3C(AND Gate).
5V is in us.

 

I need to know if you are using the HMC726LC3C as PECL or ECL?
There are many level translators for PECL. Here is one I used years ago. MC10H124. It is for TTL to ECL.
Look for level translators ECL or PECL.

I think you have data at TTL 3.3V or 5V and this part at -3.3V but some people use it with gnd=3.3 and VCC = 0V.