Description
CS3443: Simulating 4-bit MIPS ALU
You are to write a gate level simulator for a simple 4-bit ALU with the following operations:
– AND
– OR
– ADD (1-bit full adder)
– SUB
– SLT
– Overflows/zero Detection
All the operations and architectures to simulate are based on what we have studied in class. So, we’ll review them before simulation. Note that the underlying number system is two’s complement.
You may use any language of your choice to write the simulator.
1) Input format (to be input from the command line):
Opcode (in string) operand1 operand2 (both operands in integer):
e.g., ADD 11110001, SUB 11110001, AND 11110001, OR 11110001, SLT 1111 0001
2) Output format (to be displayed on the screen):
– For ADD, SUB, AND, OR:
Opcode: 4-bit result, 1-bit overflow-detection, 1-bit zero-detection
ADD: 0000,1,1
SUB: 1110,0,0
AND: 0001,0,0
OR: 1111,0,0
– For SLT:
1-bit result (0 or 1)
SLT: 0001
![Write a Python function that takes as input three integers, M, N, and r, and returns an MN matrix of rank r. Create matrices of different sizes and ranks, and use numpy.linalg.matrix_rank() to verify the returned matrices have the desired rank. Why should you expect a randomly generated matrix to have the rank you prescribe? What happens if you set r > min(M, N), and why does that happen? def randrank(M, N, r): A = random.randn(M, r) B = random.randn(N, r) return A.dot(B.T) R = randrank(32, 41, 7) print(R.shape, 'n') print(LA.matrix_rank(R), 'n') (32, 41) 7 (a) Use the function in Exercise #1 to generate a 5020 random matrix of rank r = 20, and visualize it. (b) Find the SVD of the matrix in part (a) using numpy.linalg.svd(). (c) Reconstruct the MN 2D array s with the entries of along its diagonal and zeros everywhere else: S = [s100000, s200000, sN00] if M > N, or S = [s1000, s2000, sM000000] if M < N (d) Verify that U.dot(S.dot(Vt)) recovers the matrix created in part (a). (e) Repeat (a) - (d) for a randomly generated 2050 matrix of rank r = 20.](https://gotit-pro.com/wp-content/uploads/2023/10/9d894064-eba6-456a-bd74-1f134ab849c5.png)
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