Unit 2 Solutions Unit 2 Problem Solutions
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1 Unit 2 Problem Solutions 2.1 See LD p. 731 for solution. 2.2 (a) In both cases, if = 0, the transmission is 0, and if = 1, the transmission is (b) In both cases, if = 0, the transmission is, and if = 1, the transmission is nswer is in LD p (a) = [( 1) ( 1)] E D = E D 2.4 (b) = (' ( )) = (' ) = ( ) = = 2.5 (a) ( ) ( ) (D' ) (D' E) = ( ) (D' ) (D' E) y Dist. Law = (D' ) (D' E) y Dist. Law = D' E y Dist. Law 2.5 (b) (' ') (' ' D) (' D') = (' ' D) (' D') {y Distributive Law with = ' '} = '' '' 'D 'D' 'D' DD' = '' 'D' '' 'D' 2.6 (a) 'D' = ( ') ( D') 2.6 (b) W W' = (W W' ) = ( ') ( ') ( D') ( D') = (W ) {y bsorption} = (W ) (W ) 2.6 (c) ' E DE' = ' E( D') = ' E( D) = (' E) (' D) = (' E) ( E) ( E) (' D) ( D) ( D) 2.6 (d) W' Q' = ( W' Q') = [W' ( Q')] = (W' ) (W' Q') y Distributive Law 2.6 (e) D' 'D' ' = D' ( ') ' 2.6 (f) DE = D' ( ') ' y Elimination Theorem = ( D)( E) = (D' ') ( ' ') = ( D)( D)( E)( E) = (D' ') (D' ) ( ' ') y Distributive Law and Elimination Theorem = (' D') ( D') 2.7 (a) ( D) ( E) ( ) = DE pply second Distributive Law twice 2.7 (b) W V U = (W V U) y first Distributive Law D U E V W 2.8 (a) [()' 'D]' = ('D)' = ( D') 2.8 (b) [ (' D)]' = '((' D))' = D' = '(' (' D)') = '(' D') 2.8 (c) (( ') )' ( ) ( )' = '' 'D' = (' ') ( )'' = (' ')'' = '' 2.9 (a) = [( )' ( ( )')'] ( ( )')' = ( ( )')' y Elimination Theorem with =(()')' = '( ) = ' 2.9 (b) G = {[(R S T)' PT(R S)']' T}' = (R S T)' PT(R S)' T' = T' (R'S'T') P(R'S')T = T' PR'S'T'T = T' engage Learning. ll Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
2 2.10 (a) 2.10 (b) ' 2.10 (c) 2.10 (d) ' ' ' 2.10 (e) 2.10 (f) 2.11 (a) 2.11 (c) (' ' )(' ' )' = 0 y omplementarity Law (' D)()' = ' D y Elimination Theorem 2.11 (b) 2.11 (d) (' D) (' D) = (' D) y bsorption (' D')(' EG) = ' D'EG y Distributive Law 2.11 (e) [' ( D)' E']( D) = '( D) E'( D) Distributive Law 2.11 (f) '( )(D'E )' (D'E ) = '( ) D'E y Elimination 2.12 (a) ( ') ( ')' = 1 y omplementarity 2.12 (b) [W '( )][W' ' ( )] = '( ) Law y Uniting Theorem 2.12 (c) (V'W U)' (U V'W) = (V'W U)' ( ) y Elimination Theorem 2.12 (d) (UV' W')(UV' W' ') = UV' W' y bsorption Theorem 2.12 (e) (W' )( ') (W' )'( ') = ( ') y Uniting Theorem 2.13 (a) 1 = ' ( ) = 0 = 2.13 (b) 2 = '' ' = ' ' = ' ' 2.13 (c) 3 = [( )'D][( ) D] = ( )'D ( ) ( )' D = ( )' D y bsorption 2.12 (f) 2.13 (d) 2.14 (a) ( E D) 2.14 (b) W VU (V' U W)[(W ) U'] [(W ) U' ] = (W ) U' y bsorption = [( )]' ( )D = [( )]' D y Elimination with = [( ) ]' = '' ' D' 2.15 (a) f ' = {[ (D)'][(D)' (' )]}' = [ (D)']' [(D)' (' )]' = '(D)'' (D)''[(' )]' = 'D D[' (' )'] = 'D D[' '''] = 'D D[' '] 2.15(b) f ' = [' (' D)(D' ')]' = (')'[(' D)(D' ']' = (' '' ')[(' D)' (D')'''] = (' ')['''D' (' ' D'')] = (' ')['D' (' ' D)] 2.16 (a) f D = [ (D)'][(D)' (' )] D 2.16 (b) f D = [' (' D)(D' ')] D = [ ( D)'] [( D)'( ')] = ( ' )['D ( D' )') 2.17 (a) f = [(' )] [( ')] 2.17 (b) f = ' ' ' = = ' ' ' = ' ' ' = ' ' = = 2.17 (c) f = (' ' )( )(' ' ' ) ( ') = ( ) 2.18 (a) product term, sum-of-products, product-of-sums) engage Learning. ll Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
3 2.18 (b) sum-of-products 2.18 (c) none apply 2.18 (d) sum term, sum-of-products, product-of-sums 2.18 (e) product-of-sums (a) W = D[(' ' ) ' ] 2.20 (b) = D[(' ' ) ' ] = ' D ' D ' D ' D W ' D ' D 2.20 (c) = D[(' ' ) ' ] = D(' ' ' )( ' ) = D(' ' ' )( ) D ' ' ' 2.21 H G x x x 2.22 (a) '' 'D 'DE' = '(' D DE') = '[' D( E')] = '(' D)(' E') 2.22 (d) '' (D' E) = '' ( E)(D' E) = ('' E)('' D' E) = (' E)(' E) (' D' E)(' D' E) 2.22 (b) 2.22 (c) H'I' JK = (H'I' J)(H'I' K) = (H' J)(I' J)(H' K)(I' K) ' ' D' = (' ' D') = [( )(' ') D'] = ( D')(' ' D') 2.22 (e) 2.22 (f) 2.23 (a) W U'V = (W U')(W )(W V) 2.23 (b) '' 'D' E' = '' 'D' E' = ' (' D') E' = (' E')(' D' E') = (' E)(' ')( E)( ' ) (' D' E)(' D' ') W' W'' W'' = '(W W') W'' = '(W' ) W'' = (' W')(' ')(W' W')(W' ') = (' W')(' ')(W' ) TW U' V = (TU)(T'V)(WUV)(W'V) 2.23 (c) '' 'D' 'E' = '(' D' E') 2.23 (d) = '[E' (' D')] = '(E' )(E' ' D') DE' ' = ( DE' ') = [DE' ( ')] = (DE' )(DE' ') = ( D)( E')( ' D)( ' E') engage Learning. ll Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
4 2.24 (a) [(')' (' )'] = ' (' )' = ' ' y Elimination Theorem with = (' ) 2.24 (b) ( ('( W)')')' = ''( W)' = '''W' 2.24 (d) ( )D ( )' = D ( )' 2.24 (c) [(' ')' ('')' 'D]' {y Elimination Theorem with = ( )'} = (' ')''( D') = '' = D '' 2.25 (a) (P, Q, R, S)' = [(R' PQ)S]' = R(P' Q') S' 2.25 (b) (W,,, )' = [ (W ')]' = RP' RQ' S' 2.25 (c) (,,, D)' = [' ' D]' = [' ' D]' = (' D') = [ ' W]' = [ W]' = [ ]' = '' '' 2.26 (a) = [(' )']' = [' '] = 2.26 (b) G = [()'( )]' = ( '') = 2.26 (c) H = [W''(' ')]' = W 2.27 = (V W) (V ) (V ) = (V W)(V ) = V ( W) y Distributive Law with = V W 2.28 (a) = ' ' ' = ' ' (y Uniting Theorem) = ( ') ' = ( ) ' (y Elimination Theorem) = ' = ( ') = ( ) = 2.28 (b) V eginning with the answer to (a): = ( ) lternate solutions: = ( ) = ( ) 2.29 (a) ' () ' ' (') (b) ' () () (') () (') engage Learning. ll Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
5 2-29 (c) 2.29 (e) ' ' ' (d) W W' W W'W W' W (W')(W) ' () (') 2.30 = (') '' (from the circuit) = (' '')( '') (Distributive Law) = ('')(')('')(')()(') (Distributive Law) = (1')(1)('')(')()(1) (omplementation Laws) = (1)(1)('')(')()(1) (Operations with 0 and 1) = ('')(')() (Operations with 0 and 1) ' ' G = ( ' ' )(' )( ) (from the circuit) engage Learning. ll Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
6 engage Learning. ll Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Full file at
ull file at https://fratstock.eu Unit 2 Problem Solutions Unit 2 Solutions 2.1 See LD p. 693 for solution. 2.2 (a) In both cases, if = 0, the transmission is 0, and if = 1, the transmission is 1. 2.2 (b)
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