Can I claim my assignment solutions as mini projects in my resume?

Unless your resume format is prescribed by some external entity, then you can put pretty much anything you want on it. But, don't oversell these as they were all, I assume, a year or less in duration.

And again, unless you are required to use a specific format for some reason, there is no reason for a "Project" item.

Just be clear and honest in any CV.

But perhaps you mean that your institute requires you to produce such a thing for graduation and they set the format. In that case, seek guidance locally about what is accepted and what is not.

I have seen several students add something like this to a resume. If you don't have any significant work or research experience to list, this can show off some skills. My only suggestion is to be very clear that these are class assignments. If you call them "technical projects" or something it's ambiguous as to whether it's work, research or class. Be very clear that this is classes

"Can I claim my assignment solutions as mini projects in my resume?"

You would be better off putting research-level projects with professors or industry professionals if possible, or even independent projects that you've done in your free time and posted online (for example on GitHub). But if you don't have anything like that, you can of course put down major assignment projects in your resume, but I'd recommend not to oversell these as some type of project done as a contractor for a company in industry or as a paid research internship with a professor.

Since the example you gave was for a course on computer architecture, most people looking at your resume these days will be familiar with GitHub, and for someone with a lack of "formal" project experience, it may not hurt to list some of your bigger GitHub projects, which may include projects you did for your academic courses.

"Like in my Advanced Computer Architecture course, in one of the assignments we have to build and simulate cache from the scratch and thereby analyze the entire experiment. It is more like a project than an assignment."

Sure, it's not a small assignment, but it's also still a student-level course project whose purpose is only pedagogial: It's a generic assignment which seems to be the same for everyone in the class, and has been solved several thousands of times, so there is nothing "novel" like what would be expected in a research-level project. As an undergrad, the end-of-term project for an advanced 4th year course on quantum computing, I wrote a review paper on a topic of my choice in quantum computing for which no review paper had existed.

Likewise for the final project for a 3rd year undergrad course in numerical methods for differential equations, I wrote a review on "Linear Multi-step Methods" which didn't exist at the time, and after posting it on arXiv it has received 6 citations on Google Scholar, including in some people's PhD theses.

In summary: some undergrad courses can involve quite substantial work for the assignments, ranging from generic problems to solve which may be challenging but have still been done thousands of times by other students, to full-fledged research projects like the ones described above, where it is really more of a "research project" than a generic assignment question.

Another good example is the project Adam Bookatz did for the MIT course Physics 6.845 taught by Scott Aaronson, which turned out to become the first canonical survey of QMA-complete problems. You can see at the end of the paper, that it says

"Much appreciation goes to Scott Aaronson, for whose excellent MIT 6.845 course I prepared this paper."