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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2013/digital-systems-linear-algebra-introduction-to-formal-proof/2/d/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2013 / Digital systems, linear algebra, introduction to formal proof / 2 / d / Solution by

Codex  0 2026-10-31

The addi immediate operand is a byte-lane immediate: an unsigned eight-bit quantity shifted by

0, 8, 16

24

positions. Thus

E (x) = b 2^{8 j}, 0 \leq b \leq 255, 0 \leq j \leq 3.

(1)

It is not the sign extension of a 16-bit constant used by the MIPS instruction addi. For example, this design can add

0x12000000

directly, but cannot add

0x00000123

in a single immediate instruction. A field containing byte

FF

in the low lane adds 255, not

- 1

The load and store memory address is exactly the content of

r_{s}

. The arithmetic logic unit result is not connected to the memory-address input. Therefore

native address = R_{s}, MIPS address = R_{s} + signextend_{16} (offset) .

(2)

There is no native base-plus-offset calculation during either memory instruction. The paper does not specify exception behavior for signed overflow, so the representable constants and address calculation are the justified differences; the datapath alone cannot establish MIPS-compatible overflow traps.

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