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CHAP_2_SOLUTIONS_SET_2

# CHAP_2_SOLUTIONS_SET_2 - EE 311 Digital Hardware...

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EE 311 Digital Hardware Organization Chapter 2 Homework Solutions (Set 2) 2.20 The simplest SOP implementation of the function is found as follows. ( ) ( ) ( ) [ ] ( ) [ ] F = m(3,4,6,7) = x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 2 3 1 1 1 3 2 2 2 3 1 3 Σ + + + = + + + = + + + = + 2.21 The simplest SOP implementation of the function is found as follows. ( ) ( ) ( ) [ ] ( ) [ ] ( ) ( ) F = m(1,3,4,6,7) = x x x +x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 3 2 2 1 2 3 1 2 3 3 1 3 1 2 3 1 2 1 3 1 2 3 2 1 3 1 2 2 3 1 Σ + + + = + + + + = + + + + = + + = + + = + + = ( ) ( ) 3 1 2 3 1 3 1 2 1 3 x x x Simplification Theorem: 16a x x x x x x + + = + + 2.22 The simplest POS implementation of the function is found as follows. ( ) ( ) ( ) ( ) [ ] ( ) [ ] ( ) ( ) ( ) F = M 0,2,5) = x +x +x x +x +x x +x +x x +x +x x +x +x x +x +x x +x x +x +x 1 2 3 1 2 3 1 2 3 1 3 2 1 3 2 1 2 3 1 3 1 2 3 Π ( = =

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2.23 The simplest POS implementation of the function is found as follows. ( ) ( ) ( ) ( ) ( ) [ ] ( ) [ ] ( ) [ ] ( ) [ ] ( ) ( ) F = M 0,1,5,7) = x +x +x x +x +x x +x +x x +x +x x +x +x x +x +x x +x +x x +x +x x +x x +x 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 3 2 1 3 2 1 2 1 3 Π ( = = 2.24 The simplest SOP implementation of the function is found as follows. ( ) ( ) ( ) F = x x x x x x x x x x x x x x x x x x x x x x x x = x x x x x x x x +x x x x x x x x +x x x x x x x x x x x x x x x x +x x x x x x x x x x 1 3
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CHAP_2_SOLUTIONS_SET_2 - EE 311 Digital Hardware...

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