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) =xx x xx x xxx xx x x x xx 123 23 1 1 13 2 2 23 13 Σ + ++ = +++ = = + 2.21 The simplest SOP implementation of the function is found as follows. ( ) ( ) ( ) [ ] ( ) [ ] ( ) ( ) F = m(1,3,4,6,7) =xxx +xxx x x x xx x x x 2 12 3 3 12 1 23 2 1 2 1 Σ + = ++++ = = = = = ( ) ( ) 31 x x x Simplification Theorem: 16a + + = 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 2 2 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 123 12 3 3 13 2 2 Π ( = = 2.24 The simplest SOP implementation of the function is found as follows. ( ) ( ) ( ) F=xxx xxx xxx x x xxx x x x =xxxx xxxx +xxxx xxxx xxxx xxxx +xxxx xx 134 234 134 2 2 234 1 1 123 4 4 1234 + + = + + + + + + ++ = + + + ( ) ( ) ( ) [ ] ( ) ( ) [ ] [ ] ( ) [ ] ( ) [ ] ( ) [ ] x xxx xxx +xxx xxxx xx xxx xx xx xxxx x xxx xx x xxx xxx x xxx xx+ x 34 3 124 124 341 2 1 2 41 2 1 2 1 2 2 2 2 1 2 1 31 4 1 2 4 1 2 3 = +++ = ++++ = + + = = + = + = ( ) [ ] ( ) [ ] ( ) [ ] [ ] x x x x +x Simplification Theorem: 16a xxx xx xx xx xx 14 4 1 2 4 1 4 2 4 314 4 2 4 2 4 + = = + + = + = +
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2.28 The simplest circuit implementation of the function is found as follows.
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This note was uploaded on 04/29/2008 for the course EE 101 taught by Professor Gutschlag during the Fall '07 term at Bradley.

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CHAP_2_SOLUTIONS_SET_2 - EE 311 Digital Hardware...

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