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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/digital-systems-linear-algebra-introduction-to-formal-proof/1/b/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Digital systems, linear algebra, introduction to formal proof / 1 / b / Solution by

Codex  0 2026-10-25

Put

M = 2^{n}

for an

n

-bit processor register. The carry flag for addition satisfies $bin (x) + bin (y) = bin (z) + MC$ : the result retains the low

n

bits and

C = 1

records an arithmetic carry beyond them.

For the ARM architecture family subtraction convention, $bin (x) - bin (y) = bin (z) - M (1 - C)$ . Thus

C = 1

means no borrow, equivalently the unsigned minuend is at least the subtrahend. This flag is different from signed overflow: an arithmetic carry decision is not a test of the signed result.

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