 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2018/digital-systems-linear-algebra-introduction-to-formal-proof/3/a/solution

Fetch the MIPS instruction at the program counter, and compute

p c + 4

rs

and

r t

select the two operands. The function field selects ALU addition. The result returns through write-back multiplexer input zero to destination

r d

, and the next program counter is

p c + 4

Using the diagram's actual selector encodings, the control signals are

add RegDst 1 Branch 00 Jump 0 MemWrite 0 MemToReg 0 ALUOp 10 MemRead 0 ALUSrc 0 RegWrite 1 .

Here

ALUOp = 10

00

means add and

01

means subtract. The source's

Branch = (B r_{1}, B r_{0})

is a two-bit control: the branch-taken output is

B r_{1} \land (B r_{0} \oplus Zero)

. With

B r_{1} = 0

B r_{0}

is immaterial; zero is a convenient concrete setting. No data-memory access occurs.

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