 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2021/digital-systems-linear-algebra-introduction-to-formal-proof/3/d/solution

Write the inputs as

a = 2 a_{1} + a_{0}

and

b = 2 b_{1} + b_{0}

. Each row compares the represented value of

a

with all four values of

b

. In Gray code order

00, 01, 11, 10

along both axes, the Karnaugh map is

a_{1} a_{0} \ b_{1} b_{0} 00011110 001111010111110010100011

The equality cases lie on the diagonal and are all one. A complete row of ones at

a = 3

and a complete column at

b = 0

provide useful checks. The outlined groups are used in the next part.

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