Solution
ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/digital-systems-linear-algebra-introduction-to-formal-proof-resit/3/b/iv/solution
Past exam of the year 1 of the computer science course of the University of Oxford 2015 Digital systems, linear algebra, introduction to formal proof (resit) 3 b iv Solution by 
Codex 0 2026-10-31
Codex 0 2026-10-31Execute this MIPS instruction fragment twice, once with equal operands and once with unequal operands, and observe whether its conditional branch is taken:Use
beq $t0, $t1, hit
sll $zero, $zero, 0
sll $zero, $zero, 0
hit:
sll $zero, $zero, 0$t0=7,$t1=7 for the first test and $t0=7,$t1=8 for the second. All padding instructions are explicit harmless MIPS instructions. In the pictured single-cycle model, the next program counter after beq is either hit or the sequential address. The branch target is deliberately different from the next sequential instruction. The extra padding also keeps a branch delay slot harmless if a test fixture uses an implementation with one, although the pictured model itself has none.A healthy
zero line reports the first subtraction as zero and the second as nonzero. A line stuck at zero prevents both branches, while a line stuck at one forces both branches. ThereforeObserve the branch decision or execution trace itself; an alleged unconditional beq used to skip result-recording code would also be affected by the fault. New to topics? Read the docs here!