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That is too complex a question for this forum. If you are willing to pay, there no doubt are some who would take on the job. When I was working, we did that sort of thing, using a minicomputer running a customized BASIC program, programmable power supplies, programmable signal generator, timer- counter, etc.
It's too general a question, Aniketrane. What specific IC's do you want to test? (logic & timers make up a very broad category) Are you looking for a GO/noGO type test fixture? Is it intended for use in high volume applications? Why do you think it's needed? Answer these kinds of questions, and you'll get better answers.
If you're just trying to figure out how things work, search the forums. There is plenty of information here on the operation of various logic and timer ICs. If you can't find what you're looking for, ask a specific question. You'll find plenty of people here willing to help
You could build something in software using Parallel Port.
Simply set up a program using VB/C# whatever that allows you write binary 1 or 0 to a pin and then read in the data using the LPT ports EPP register. Then create your code to allow for configuring the tests for example. Test #1 for And Gate. Write 1 to pin 1 and 0 to pin 2, then call EPP read to see what the value on pin 3 is. If it is 0 then proceed to next test. Etc. This way you could use configuration files to test different types of chips. If you had more information I could give you a better example, but as others have said this is a little vague.