MIPS Factorial & Binomial Coefficients

This repository is a project for the Computer Architecture course at Harokopio University of Athens – Dept. of Informatics and Telematics. It contains several implementations of the factorial function in MIPS assembly, as well as applications to the binomial theorem.
The programs demonstrate recursion, stack usage, function calls, and arithmetic operations in MIPS.

Contents

• factorial/factorial1.asm: Basic recursive factorial implementation (example: factorial of 3).
• factorial/factorial2_1.asm: Computes a single binomial coefficient (example: C(5,2) = 10).
• factorial/factorial2_2.asm: Computes all binomial coefficients for n = 5 in a loop.
• factorial/factorial3.asm: Alternative recursive factorial implementation with clearer stack handling.

Documentation

• docs/report_el.pdf: Detailed report describing the logic and implementation of factorial2_1.asm and factorial2_2.asm (including theory, code, and MARS execution snapshots).

How to Run

1. Open MARS (or SPIM).
2. Load the .asm file you want to run.
3. Click Assemble and then Run.

Expected Output

• factorial1.asm prints 6 (3! = 6)
• factorial2_1.asm prints 10 (since C(5,2) = 10)
• factorial2_2.asm prints sequence: 1,5,10,10,5,1
• factorial3.asm prints factorial of 3 (6)

Learning Outcomes

• Understanding recursion in MIPS assembly
• Using the stack ($sp) to store arguments and return addresses
• Implementing factorial with recursive calls
• Applying factorial to compute binomial coefficients
• Printing results via syscall

Author

• Name: Exarchou Athos
• Student ID: it2022134
• Email: it2022134@hua.gr, athosexarhou@gmail.com

License

This project is licensed under the MIT License.