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1 ull file at 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 (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 Th. 8D = (D' ) (D' E) y Th. 8D = D' E y Th. 8D 2.5 (b) (' ') (' ' D) (' D') = (' ' D) (' D') {y Th. 8D with = ' '} = '' '' 'D 'D' 'D' DD' = '' 'D' '' 'D' 2.6 (a) 'D' = ( ') ( D') 2.6 (b) ' = ( ' ) = ( ') ( ') ( D') ( D') = ( ) {y Th. 10} = ( ) ( ) 2.6 (c) ' E DE' = ' E( D') = ' E( D) = (' E) (' D) = (' E) ( E) ( E) (' D) ( D) ( D) 2.6 (d) ' Q' = ( ' Q') = [' ( Q')] = (' ) (' Q') y Th. 8D 2.6 (e) D' 'D' ' = D' ( ') ' = D' ( ') ' y Th. 11D = (D' ') ( ' ') = (D' ') (D' ) ( ' ') y Th. 11D = (' D') ( D') 2.6 (f) DE = ( D)( E) = ( D)( D)( E)( E) 2.7 (a) ( D) ( E) ( ) 2.7 (b) V U = ( V U) = DE y first distributive law (Th. 8) pply second distributive law (Th. 8D) twice D E 2.8 (a) [()' 'D]' = ('D)' = ( D') 2.8 (b) [ (' D)]' = '((' D))' = D' = '(' (' D)') = '(' D') 2.8 (c) (( ') )' ( ) ( )' = '' 'D' = (' ') ( )'' = (' ')'' = '' 2.9 (a) = [( )' ( ( )')'] ( ( )')' 2.9 (b) G = {[(R S T)' PT(R S)']' T}' = ( ( )')' = (R S T)' PT(R S)' T' y Th. 10D with =(()')' = '( ) = ' = T' (R'S'T') P(R'S')T = T' PR'S'T'T = T' U V 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 Unit 2 Solutions ull file at (a) 2.10 (b) ' 2.10 (c) 2.10 (d) ' ' ' 2.10 (e) 2.10 (f) 2.11 (a) (' ' )(' ' )' = 0 y Th. 5D 2.11 (b) (' D) (' D) = (' D) y Th (c) (' D)()' = ' D y Th. 11D 2.11 (d) (' D')(' EG) = ' D'EG y Th. 8D 2.11 (e) [' ( D)' E']( D) = '( D) E'( D) y Th (f) '( )(D'E )' (D'E ) = '( ) D'E y Th. 11D 2.12 (a) ( ') ( ')' = 1 y Th (b) [ '( )][' ' ( )] = '( ) y Th. 9D 2.12 (c) (V' U)' (U V') = (V' U)' ( ) y Th (d) (UV' ')(UV' ' ') = UV' ' y Th. 10D 2.12 (e) (' )( ') (' )'( ') = ( ') y Th (a) 1 = ' ( ) = 0 = 2.13 (b) 2 = '' ' = ' ' = ' ' 2.13 (c) 3 = [( )'D][( ) D] = ( )'D ( ) ( )' D = ( )' D y Th. 5D & Th. 2D 2.12 (f) 2.13 (d) 2.14 (a) ( E D) 2.14 (b) VU (V' U )[( ) U'] [( ) U' ] = ( ) U' y Th. 10 = [( )]' ( )D = [( )]' D y Th. 11D 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) ull file at sum-of-products 2.18 (c) none apply Unit 2 Solutions 2.18 (d) sum term, sum-of-products, product-of-sums 2.18 (e) product-of-sums (a) = D[(' ' ) ' ] = D[(' ' ) ' ] 2.20 (b) = ' D ' D ' D ' D ' 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) U'V = ( U')( )( V) 2.23 (b) '' 'D' E' = '' 'D' E' = ' (' D') E' = (' E')(' D' E') = (' E)(' ')( E)( ' ) (' D' E)(' D' ') ' '' '' = '( ') '' = '(' ) '' = (' ')(' ')(' ')(' ') = (' ')(' ')(' ) T U' V = (TU)(T'V)(UV)('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 Unit 2 Solutions ull file at (a) [(')' (' )'] = ' (' )' 2.24 (b) ( ('( )')')' = ''( )' = '''' = ' ' y Th. 11D with = (' ) 2.24 (c) 2.25 (a) 2.25 (c) [(' ')' ('')' 'D]' = (' ')''( D') = '' (P, Q, R, S)' = [(R' PQ)S]' = R(P' Q') S' = RP' RQ' S' (,,, D)' = [' ' D]' = [' ' D]' = (' D') 2.24 (d) 2.25 (b) ( ) D ( )' = D ( )' {y Th. 11D with = ( )'} = D '' (,,, )' = [ ( ')]' = [ ' ]' = [ ]' = [ ]' = '' '' 2.26 (a) = [(' )']' = [' '] = 2.26 (b) G = [()'( )]' = ( '') = 2.26 (c) H = [''(' ')]' = 2.27 = (V ) (V ) (V ) = (V )(V ) = V ( ) y Th. 8D with = V 2.28 (a) = ' ' ' = ' ' (y Th. 9) = ( ') ' = ( ) ' (y Th. 11D) = ' = ( ') = ( ) = 2.28 (b) V eginning with the answer to (a): = ( ) lternate solutions: = ( ) = ( ) 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 ull file at (a) ' () ' ' 2.29 (b) (') Unit 2 Solutions ' () () (') () (') (c) ' ' ' (d) ' () (') ' ' (e) ' ' ' (')() = (') '' (from the circuit) = (' '')( '') (distributive law) = ('')(')('')(')()(') (distributive law) = (1')(1)('')(')()(1) (complementation laws) = (1)(1)('')(')()(1) (0 and 1 operations) = ('')(')() (0 and 1 operations) 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 Unit 2 Solutions ull file at engage Learning. ll Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

Unit 2 Solutions Unit 2 Problem Solutions

Unit 2 Solutions Unit 2 Problem Solutions 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 1. 2.2 (b) In both cases, if = 0, the transmission is, and