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

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- Solution 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.

Figure 1.
Two-bit comparator Karnaugh map with all five essential four-cell groups
. Details.

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