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 $pc+4$. The opcode selects an MIPS R-type instruction; register-file read addresses $rs$ and $rt$ select the two operands. The function field selects ALU addition. The result returns through write-back multiplexer input zero to destination $rd$, and the next program counter is $pc+4$.

Using the diagram's actual selector encodings, the control signals areHere $\mathrm{ALUOp}=10$ means decode the function field; $00$ means add and $01$ means subtract. The source's $\mathrm{Branch}=(B{r}_1,B{r}_0)$ is a two-bit control: the branch-taken output is $B{r}_1\wedge (B{r}_0\oplus \mathrm{Zero})$. With $B{r}_1=0$, $B{r}_0$ is immaterial; zero is a convenient concrete setting. No data-memory access occurs.