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Sol_hw3[1]

# Sol_hw3[1] - 2.10(5 points Let f = m(1 2 3 4 5 6 7 The...

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Unformatted text preview: 2.10 (5 points) Let f = m(1, 2, 3, 4, 5, 6, 7). The canonical sum-of-products for f is given by f = x 1 ' x 2 ' x 3 + x 1 ' x 2 x 3 ' + x 1 ' x 2 x 3 + x 1 x 2 ' x 3 ' + x 1 x 2 ' x 3 + x 1 x 2 x 3 ' + x 1 x 2 x 3 It can be manipulated as follows: f = m(4, 5, 6, 7) + m(2, 3, 6, 7) + m(1, 3, 5, 7) = (x 1 x 2 ' x 3 ' + x 1 x 2 ' x 3 + x 1 x 2 x 3 ' + x 1 x 2 x 3 ) + ( x 1 ' x 2 x 3 ' + x 1 ' x 2 x 3 + x 1 x 2 x 3 ' + x 1 x 2 x 3 ) + ( x 1 ' x 2 ' x 3 + x 1 ' x 2 x 3 + x 1 x 2 ' x 3 + x 1 x 2 x 3 ) = x 1 ( x 2 ' x 3 ' + x 2 ' x 3 + x 2 x 3 ' + x 2 x 3 ) + x 2 (x 1 ' x 3 ' + x 1 ' x 3 + x 1 x 3 ' + x 1 x 3 ) + x 3 (x 1 ' x 2 ' + x 1 ' x 2 + x 1 x 2 ' + x 1 x 2 ) = x 1 ( x 2 ' (x 3 ' + x 3 ) + x 2 (x 3 ' + x 3 )) + x 2 (x 1 ' (x 3 ' + x 3 ) + x 1 (x 3 ' + x 3 )) + x 3 (x 1 ' (x 2 ' + x 2 ) + x 1 (x 2 ' + x 2 )) = x 1 + x 2 + x 3 2.11 (5 points) Let f = M(0, 1, 2, 3, 4, 5, 6). The canonical sum-of-products for f is given by f = (x 1 + x 2 + x 3 ) (x 1 + x 2 + x 3 ') (x 1 + x 2 ' + x 3 ) (x 1 + x 2 ' + x 3 ') (x 1 ' + x 2 + x 3 )• (x 1 ' + x 2 + x 3 ') (x 1 ' + x 2 ' + x 3 ) It can be manipulated as follows: f = M(0, 1, 2, 3) • M(0, 1, 4, 5) • M(0, 2, 4, 6) = ((x 1 + x 2 + x 3 ) (x 1 + x 2 + x 3 ') (x 1 + x 2 ' + x 3 ) (x 1 + x 2 ' + x 3 '))• ((x 1 + x 2 + x 3 ) (x 1 + x 2 + x 3 ') (x 1 ' + x 2 + x 3 ) (x 1 ' + x 2 + x 3 '))• ((x 1 + x 2 + x 3 ) (x 1 + x 2 ' + x 3 ) (x 1 ' + x 2 + x 3 )(x 1 ' + x 2 ' + x 3 )) = ((x 1 + x 2 + x 3 ) (x 1 + x 2 + x 3 ') (x 1 + x 2 ' + x 3 ) (x 1 + x 2 ' + x 3 '))' ' • ((x 1 + x 2 + x 3 ) (x 1 + x 2 + x 3 ') (x 1 ' + x 2 + x 3 ) (x 1 ' + x 2 + x 3 '))' ' • ((x 1 + x 2 + x 3 ) (x 1 + x 2 ' + x 3 ) (x 1 ' + x 2 + x 3 )(x 1 ' + x 2 ' + x 3 ))' '...
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Sol_hw3[1] - 2.10(5 points Let f = m(1 2 3 4 5 6 7 The...

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