Question

create a MIPS program that demonstrates that the associative law fails in addition for floating point numbers (single or double precision). You only need to demonstrate it for single precision. Remember the associative law is a + (b + c) = (a + b) + c

Answer 1

The question involves writing a MIPS assembly language program to demonstrate that the associative law for floating point addition (a + (b + c) = (a + b) + c) can fail due to rounding errors and finite precision of numbers. A program would calculate both sequences of addition and then compare the results to show the difference.

Step-by-step explanation:

The question pertains to demonstrating that the associative law fails for floating point numbers in the MIPS assembly language. In mathematics, the associative law for addition suggests that a + (b + c) = (a + b) + c should always hold true. However, in computer arithmetic, especially with floating point numbers, this law can fail due to rounding errors and the finite precision of numbers.

To showcase this, one could write a MIPS assembly program that performs floating point addition in both associative sequences and compares the results. The program would load three single precision floating point numbers into the floating point registers, say $f0, $f1, and $f2. It would first compute b + c into a temporary register, add the result to a, and store it. Then it would compute a + b into a temporary register, add c to it, and store it. Finally, the program would compare the two stored results to demonstrate the discrepancy.

This is an example of computer science concepts applied in the practical context of MIPS architecture, which could lead to important considerations in software development and numerical computations where precision is critical.