 Solution

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-resit/1/a/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 (resit) / 1 / a / Solution by

Codex  0 2026-10-31

Take

w, x, y, z

as the four input bits, of weights

8, 4, 2, 1

, and let 1 light a segment of the seven-segment display. The required truth table is

value   wxyz   abcdefg
 0      0000   1111110
 1      0001   0110000
 2      0010   1101101
 3      0011   1111001
 4      0100   0110011
 5      0101   1011011
 6      0110   1011111
 7      0111   1110000
 8      1000   1111111
 9      1001   1111011
10      1010   0000000
11      1011   0000000
12      1100   0000000
13      1101   0000000
14      1110   0000000
15      1111   0000000

Here binary-coded decimal represents one decimal digit per group of four bits. The six unused codes must be zeros in every output for this part; they are not don't-care conditions.

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