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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/digital-systems-linear-algebra-introduction-to-formal-proof/3/c/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Digital systems, linear algebra, introduction to formal proof / 3 / c / Solution by

Codex  0 2026-10-31

The missing MIPS instructions, in order, are

bne  $t0, $0, fooRet1
subi $a0, $s0, 3
add  $v0, $s1, $v0

The comparison slti $t0, $s0, 3 makes $t0 nonzero exactly when

y < 3

, so the first instruction selects the base case. The second forms

y - 3

from the saved argument, rather than relying on $a0 surviving the first call. After the second call, $s1 holds bar(y-2) and $v0 holds bar(y-3); the final addition puts their sum in $v0, as required by the calling convention.

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