SOLUTIONS MANUAL DIGITAL DESIGN FOURTH EDITION M. MORRIS MANO California State University, Los Angeles MICHAEL D.
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1 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ SOLUTIONS MNUL IGITL ESIGN FOURTH EITION M. MORRIS MNO alifornia State University, Los ngeles MIHEL. ILETTI University of olorado, olorado Springs rev /2/27 igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
2 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ HPTER. ase-: Octal: He: E F 2 ase (a) 32,768 (b) 67,8,864 (c) 6,87,947,674.3 (43) 5 = 4 * * * 5 = 58 (98) 2 = * * * 2 = 26 (735) 8 = 7 * * * 8 = 477 (525) 6 = 5 * * * 6 = bit binary: ecimal: = 6,383 Headecimal: 3FFF 6.5 Let b = base (a) 4/2 = (b + 4)/2 = 5, so b = 6 (b) 54/4 = (5*b + 4)/4 = b + 3, so 5 * b = 52 4, and b = 8 (c) (2 *b + 4) + (b + 7) = 4b, so b =.6 ( 3)( 6) = 2 (6 + 3) + 6*3 = Therefore: = b + m so b = 8 lso, 6*3 = (8) = (22) E = = = (64276) 8.8 (a) Results of repeated division by 2 (quotients are followed by remainders): 43 = 25(); 7(); 53(); 26(); 3(); 6() 3() () nswer: _ 2 = F 6 (b) Results of repeated division by 6: 43 = 26(5); () (Faster) nswer: F = _.9 (a). 2 = = (b) = *(.65) = (c) = 2 * /8 + 4/64 = igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
3 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (d) FF. 6 = 5*6 3 + * *6 + + /6 = 64, (e). 2 = =.625. (a). 2 =. 2 =.9 6 = + 9/6 =.563 (b). 2 =. 2 = = 6 + 4/6 = 6.25 Reason:. 2 is the same as. 2 shifted to the left by two places.... The quotient is carried to two decimal places, giving. hecking: 2 / 2 = 59 / 5. 2 = (a) and + = 6 = 55 (b) 62 h and 958 h 2E h _ 2E h +34 h _ 34 h 62 h _ = h = (a) onvert to binary: Integer Remainder oefficient Quotient 27/2 = 3 + ½ a = 3/2 6 + ½ a = 6/2 3 + a 2 = 3/2 + ½ a 3 = ½ + ½ a 4 = igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
4 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ = 2 Integer Fraction oefficient.35 2 = +.63 a - =.63 2 = +.26 a -2 =.26 2 = +.52 a -3 =.52 2 = +.4 a -4 = = = (b) 2/ Integer Fraction oefficient.6666_6666_67 2 = _3333_34 a - = = a -2 = = a -3 = = a -4 = = a -5 = = a -6 = = a -7 = = a -8 = = = =._ 2 =. 6 = /6 + /256 =.664 (Same as (b))..4 (a) _ (b) _ (c) _ s comp: _ s comp: _ s comp: _ 2s comp: _ 2s comp: _ 2s comp: _ (d) _ (e) _ (f) _ s comp: _ s comp: _ s comp: _ 2s comp: _ 2s comp: _ 2s comp: _.5 (a) 52,784,63 (b) 63,325,6 9s comp: 47,25,369 9s comp: 36,674,399 s comp: 47,25,37 s comp: 36,674,4 (c) 25,, (d),, 9s comp: 74,999,999 9s comp: 99,999,999 s comp: 75,, s comp:,,.6 2F 2F: 5s comp: 45 s comp: 6s comp: 46 2s comp: = 46.7 (a) (9s comp) 9659 (s comp) = = 39 (b) (9s comp) 982 ( comp) 25 8 = = (negative) Magnitude: 675 Result: 25 8 = 675 igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
5 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (c) (9s comp) (s comp) = = 9589 (Negative) Magnitude: 49 Result: = -49 (d) (9s comp) (s comp) = = 886 (Positive) Result: = Note: onsider sign etension with 2s complement arithmetic. (a) (b) s comp: s comp: with sign etension 2s comp: 2s comp: iff: sign bit indicates that the result is negative 2s complement - result (c) (d) s comp: s comp: with sign etension 2s comp: 2s comp: iff: (negative) sign bit indicates that the result is positive (2s comp) heck: 48-2 = 27 - (diff is -3) ; +8 8; ; (a) (+9286) + (_8) = = 87 (b) (+9286) + (-8) = = 8485 (c) (-9286) + (+8) = = 9955 (d) (-9286) + (-8) = = _ (Needs leading zero indicate + value); +29 _ (Leading indicates + value) -49 _; -29 _ (a) (+29) + (-49) = _ + _ = _ ( indicates negative value.) Magnitude = _; Result (+29) + (-49) = -2 (b) (-29) + (+49) = _ + _ = _ ( indicates positive value) (-29) + (+49) = +2 (c) Must increase word size by (sign etension) to accomodate overflow of values: (-29) + (-49) = _ + _ = _ ( indicates negative result) Magnitude: _ = 78 Result: (-29) + (-49) = -78 igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
6 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (9's comp) (s) comp (9's comp) (s) comp (a) (+9742) + (+64) 383 (b) (+9742) + (-64) = 92 Result: (+9742) + (-64) = 92 (c) -9742) + (+64) = = (negative) Magnitude: 9 Result: (-9742) + (64) = -9 (d) (-9742) + (-64) = = (Negative) Magnitude: 383 Result: (-9742) + (-64) = ,723 : SII:.23 ( 842) (+537) (,379).24 (a) (b) 6 3 ecimal (or ) (or ) ecimal (or ) (a) 5,37 : (b) Ecess-3: (c) 242: (d) 63:.26 5,37 9s omp: 4, code: s comp: same as (c) in.25 igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
7 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ For a deck with 52 cards, we need 6 bits (32 < 52 < 64). Let the msb's select the suit (e.g., diamonds, hearts, clubs, spades are encoded respectively as,,, and. The remaining four bits select the "number" of the card. Eample: (ace) through (9), plus through (jack, queen, king). This a jack of spades might be coded as _. (Note: only 52 out of 64 patterns are used.).28 G (dot) (space) o o l e.29 ill Gates.3 73 F4 E5 76 E5 4 EF : s F4: t E5: e 76: v E5: e 4: j EF: o 62: b 73: s = 94 printing characters.32 bit 6 from the right.33 (a) 897 (b) 564 (c) 87 (d) 2,99.34 SII for decimal digits with odd parity: (): (): (2): (3): (4): (5): (6): (7): (8): (9):.35 (a) a b c a f b g c f g.36 a b a f b g f g igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
8 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ HPTER 2 2. (a) y z + y + z ( + y + z)' ' y' z' ' y' z' y z (yz) (yz)' ' y' z' ' + y' + z' (b) (c) y z + yz ( + y) ( + z) ( + y)( + z) y z (y + z) y z y + z (c) (d) y z y + z + (y + z) ( + y) ( + y) + z y z yz (yz) y (y)z 2.2 (a) y + y' = (y + y') = (b) ( + y)( + y') = + yy' = ( +y') + y( + y') = + y' + y + yy' = (c) yz + 'y + yz' = y(z + z') + 'y = y + 'y = y (d) ( + )'(' + ') = ('')( ) = ('')() = '(') = (e) yz' + 'yz + yz + 'yz' = y(z + z') + 'y(z + z') = y + 'y = y (f) ( + y + z')(' + y' + z) = ' + y' + z + 'y + yy' + yz + 'z' + y'z' + zz' = = y' + z + 'y + yz + 'z' + y'z' = y + ( z)' + (y z)' 2.3 (a) + ' + ' = + ' = igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
9 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (b) 'yz + z = ('y + )z = z( + ')( + y) = z( + y) (c) ( + y)'(' + y') = 'y'(' + y') = 'y' (d) y + (wz + wz') = (y +wz + wz') = (w + y) (e) (' + ')(' + ') = '' + '' + '' + '' = (f) ( + y' + z')(' + z') =' + z' + 'y' + y'z' + 'z' + z'z' = z' + y'(' + z') = z' + 'y' 2.4 (a) '' + + ' = ' + = ( + ')(' + ) = + ' (b) ('y' + z)' + z + y + wz = ('y')'z' + z + y + wz =[ ( + y)z' + z] + y + wz = = (z + z')(z + + y) + y + wz = z + wz + + y + y = z( + w) + ( + y) + y = + y + z (c) '(' + ') + ( + ') = ('' + '' + + ') = ('' + + '( + ') = ( + '(' + )) = ( + ') = (d) (' + )(' + ')( + + ') = (' + ')( + + ') = '( + + ') = ' + ' + '' = '( + ') (e) + ' + ' = + ' = 2.5 (a) y F simplified F (b) y F simplified F (c) igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
10 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ y z F simplified F (d) F simplified F (e) y z F simplified F (f) igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
11 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ y z F F simplified 2.6 (a) F F simplified (b) y z F F simplified (c) y F F simplified igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
12 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (d) w y z F F simplified (e) F simplified = F (f) w y z F F simplified 2.7 (a) F F simplified igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
13 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (b) w y z F F simplified (c) F F simplified (d) F F simplified igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
14 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (e) F F simplified 2.8 F' = (w + yz)' = (w)'(yz)' = (w' + ')(y' + z') FF' = w(w' + ')(y' + z') + yz(w' + ')(y' + z') = F + F' = w + yz + (w + yz)' = + ' = with = w + yz 2.9 (a) F' = (y' + 'y)' = (y')'('y)' = (' + y)( + y') = y + 'y' (b) F' = [(' + )E' + E]' = [(' + ) + E]' = (' + )'E' = (')'()'E' F' = ( + ')(' + ')E' = 'E' + 'E' + ''E' + ''E' (c) F' = [(' + y + z')( + y')( + z)]' = (' + y + z')' + ( + y')' + ( + z)' = F' = y'z + 'y + 'z' 2. (a) F + F 2 = m i + i = (m i + i ) (b) F F2 = m i m j where m i m j = if i j and m i m j = if i = j 2. (a) F(, y, z) = (, 4, 5, 6, 7) (b) F(, y, z) = (, 2, 3, 7) F = y + y' + y'z y z F F = 'z' + yz y z F 2.2 = _ = _ (a) N = _ (b) OR = _ (c) XOR = _ igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
15 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (d) NOT = _ (e) NOT = _ 2.3 (a) Y = + + '(a + ') (b) Y = ( or ) + ' (c) Y = + + (d) Y = ( or )' + (e) Y = ('+ ') + ') (f) Y = (+ ')' + ) igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
16 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (a) y z F =y + 'y' + y'z (b) y z F = y + 'y' + y'z = (' + y')' + ( + y)' + (y + z')' (c) y z F = y + 'y' + y'z = [(y)' ('y')' (y'z)']' (d) y z F = y + 'y' + y'z = [(y)' ('y')' (y'z)']' igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
17 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (e) y z F = y + 'y' + y'z = (' + y')' + ( + y)' + (y + z')' 2.5 (a) T = ''' + '' + '' = ''(' + ) +''(' + ) = '' +'' = '(' + ') (b) T 2 =T ' = ' + '' + ' + ' + = (' + ) + '(' + ) + (' + ) = + ' + = + (' + ) = + (3,5,6,7) (,,2,4) T = ''' + '' + '' T 2 = ' + '' + ' + ' + '' '' T = '' '' = '(' + ') ' T 2 =' + + = (a) F(,, ) = ''' + '' + '' + ' + '' + ' + ' + = '('' + ' + ' + ) + (('' + ' + ' + ) = (' + )('' + ' + ' + ) = '' + ' + ' + = '(' + ) + (' + ) = ' + = (b) F(, 2, 3,..., n ) = m i has 2 n /2 minterms with and 2 n /2 minterms with ', which can be factored and removed as in (a). The remaining 2 n- product terms will have 2 n- /2 minterms with 2 and 2 n- /2 minterms with ' 2, which and be factored to remove 2 and ' 2. continue this process until the last term is left and n + ' n =. lternatively, by induction, F can be written as F = n G + ' n G with G =. So F = ( n + ' n )G =. 2.7 (a) (y + z)(y + z) = y + yz + yz + z = (3, 5, 6, 7) = (,, 2, 4) (b) (' + )(' + ) = '' + ' + = (,, 3, 7) = (2, 4, 5, 6) (c) y'z + wy' + wz' + w''z = (, 3, 5, 9, 2, 3, 4) = (, 2, 4, 6, 7, 8,,, 5) (d) (y + yz' + 'z)( + z) = y + yz' + yz + 'z = (, 3, 9,, 4, 5) = (, 2, 4, 5, 6, 7, 8,, 2, 3) igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
18 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (a) w y z F F = y'z + 'y'z + w'y + w'y + wy F = (, 5, 6, 7, 9,, 3, 4, 5 ) (b) y' z ' y' z w' y w ' y w y 5 - Three-input N gates 2 - Three-input OR gates lternative: - Five-input OR gate 4 - Inverters F (c) F = y'z + 'y'z + w'y + w'y + wy = y'z + y + wy = y z + y(w + ) (d) F = y'z + yw + y) = (, 5, 9, 3,,, 3, 5, 6, 7, 4, 5) = (, 5, 6, 7, 9,,, 3, 4, 5) (e) y' z w y F Inverter, 2 Two-input N gates, 2 Two-input OR gates igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
19 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ F = ' + ' + -'- = = 3 = 9 = '-- = = 3 = 5 = 7 -- = 5 = 7 = 3 = 5 F = (, 3, 5, 7, 9,,3, 5) = (, 2, 4, 6, 8,, 2, 4) 2.2 (a) F(,,, ) = (3, 5, 9,, 5) F'(,,, ) = (,, 2, 4, 6, 7, 8,, 2, 3, 4) (b) F(, y, z) = (2, 4, 5, 7) F' = (2, 4, 5, 7) 2.2 (a) F(, y, z) = (2, 5, 6) = (,, 3, 4, 7) (b) F(,,, ) = (,, 2, 4, 7, 9, 2) = (3, 5, 6, 8,,, 3, 4, 5) 2.22 (a) ( + )( + ') = + + ' + ' = ( + ') + = + (SOP form) = ( + ) (POS form) (b) ' + ( + y')(y + z') = (' + )[' + ( + y')(y + z')] = = (' + + y')(' + y + z') = + y + z 2.23 (a) ' + + F igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
20 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (b) ( + )( + )(' + + ) F (c) ( + '')(' + ') F (d) + + ( + ')(' + ) F 2.24 y = 'y + y' and ( y)' = ( + y')(' + y) ual of 'y + y' = (' + y)( + y') = ( y)' 2.25 (a) y = y' y = 'y Not commutative ( y) z = y'z' (y z) = (yz')' = y' + z Not associative igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
21 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (b) ( y) = y' + 'y = y = y' + y' ommutative ( y) z = (, 2, 4, 7) = (y z) ssociative 2.26 Gate NN (Positive logic) NOR (Negative logic) y z y z y z L L L H H L H H H H H L Gate NOR (Positive logic) NN (Negative logic) y z y z y z L L L H H L H H H L L L 2.27 f = a'b'c + a'bc + abc' + abc f 2 = a'bc' + a'bc + ab'c' + ab'c + abc' a' b' c' a' b c a b c' a b c a' b c' a b' c' a b' c f f 2 igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
22 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (a) y = a(bcd)'e = a(b' + c' + d')e y = a(b' + c' + d')e = ab e + ac e + ad e = ( 7, 9, 2, 23, 25, 27, 29) a bcde y a bcde y (b) y = a (c + d + e)= a'(c + d +e) + a(c'd'e') = a'c + a'd + a'e + ac'd'e' y 2 = b'(c + d + e)f = b'cf + b'df + b'ef y = a (c + d + e) = a'(c + d +e) + a(c'd'e') = a'c + a'd + a'e + ac'd'e' y 2 = b'(c + d + e)f = b'cf + b'df + b'ef a'-c--- = 8 = 9 = = a'--d-- = 8 = 9 = = a'---e- = 2 = 3 = 6 = 7 a-c'd'e'- = 32 = 33 = 34 = 35 = 2 = 3 = 4 = 5 = 2 = 3 = 4 = 5 = = = 4 = 5 -b' c--f -b' -d-f -b' --ef = 24 = 25 = 26 = 27 = 28 = 29 = 3 = 3 = 2 = 2 = 22 = 23 = 28 = 29 = 3 = 3 = 8 = 9 = 22 = 23 = 26 = 27 = 3 = 3 = 9 = = 3 = 5 = 4 = 43 = 45 = 47 = 9 = = 3 = 5 = 4 = 43 = 45 = 47 = 3 = 7 = = 5 = 35 = 39 = 5 = 55 igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
23 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ y = (2, 3, 6, 7, 8, 9,,, 2, 3, 4, 5, 8, 9, 22, 23, 24, 25, 26, 27, 28, 29, 3, 3, 32, 33, 34, 35 ) y 2 = (3, 7, 9, 3, 5, 35, 39, 4, 43, 45, 47, 5, 55) ab cdef y y 2 ab cdef y y 2 ab cdef y y 2 ab cdef y y 2 igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
24 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ hapter 3 3. yz m m y yz m m y (a) z F = y + z' (b) z F = z' + 'y yz m m y yz m m y z z (c) F = ' + yz (d) F = y + z + yz 3.2 yz y yz y m m m m z z (a) F = 'y' + z (b) F = y + 'z yz m m y yz m m y z (c) F = 'y' + y (d) F = y' + 'z z igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
25 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ yz m m y yz m m y z (e) F = z (f) F = + y' z z 3.3 yz y yz y m m m m (a) z F =y + 'y'z' + 'yz' F = y + ' z' (b) z F = 'y' + yz + 'yz' F = ' + yz yz m m y yz m m y (c) z F = 'y + yz' + y'z' F = = ' y + z' (d) z F = yz + 'y'z + yz' F = 'y'z + y igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
26 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ m m yz m m y m 8 m 9 m m z (a) F = y (b) F = + ' ' m m w yz m m y m 8 m 9 m m w m 8 m 9 m m z (c) F = + + (d) F = w''y +w w yz y w yz y m m m m w m 8 m 9 m m w m 8 m 9 m m (e) z F = w' + w'y'z (f) z F = 'y' + w'y'z igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
27 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ w yz y m m m m w m 8 m 9 m m m 8 m 9 m m z (a) F =z' + w'y'z+ wy (b) F = ' + ' ' + '' w yz y m m m m w m 8 m 9 m m m 8 m 9 m m z (c) F =w'y' + w' y' + w'y (d) F = + ' + ' ' or = + '' + '' 3.6 m m m 3 w yz m m y m 8 m 9 m m w m 8 m 9 m m z (a) F = ' ' +' + ' (b) F = y' +'z + w'y igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
28 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ m m m 3 m m m 3 m 8 m 9 m m m 8 m 9 m m (c) F = '' + + ' + ' (d) F = ''' + ' + ' + ' 3.7 w yz y m m m m w m 8 m 9 m m m 8 m 9 m m z (a) F = z + 'y (b) F = ' + ' + ' m m m 3 w yz m m y m 8 m 9 m m w m 8 m 9 m m z (c) F = '' + + ' + (or ') (d) F = w + 'y + yz igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
29 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (a) F(, y, z) = (3, 5, 6, 7) yz m m y z (b) F = (, 3, 5, 9, 2, 3, 4) m m m 8 m 9 m m (c) F = (,, 2, 3,, 2, 4, 5) w y m m w m 8 m 9 m m z igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
30 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (d) F= (3, 4, 5, 7,, 2) m m m 8 m 9 m m 3.9 (a) w yz m m y (b) m m w m 8 m 9 m m m 8 m 9 m m z Essential: z, 'z' Non-essential: w', w'z' F = z + 'z' + (w' or w'z') Essential: '',, ' Non-essential:, ' F = '' + + ' + ( OR ') (c) m m (d) yz w m m y m 8 m 9 m m w m 8 m 9 m m z Essential: ',, '' F = ' + + '' Essential: wy', y, w''z F = wy' + y + w''z igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
31 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (e) m m (f) w yz y m m m 8 m 9 m m w m 8 m 9 m m z Essential:, ', ''' F = + ' + ''' Essential: wy', w, 'z', yz F = wy' + w + 'z' + yz 3. (a) w yz m m y (b) m m w m 8 m 9 m m m 8 m 9 m m Essential: z, w', 'z' F = z + w' + 'z' z Essential:, '',, ' F = + '' + + ' igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
32 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (c) m m (d) w yz m m y m 8 m 9 m m w m 8 m 9 m m z Essential: ', Non-essential:,,, F = + + Essential: wy', y Non-essential: w, 'y'z, w'wz, w''z F = wy' + y + w''z (e) m m (f) w yz y m m m 8 m 9 m m w m 8 m 9 m m Essential:, ', ' Non-essential: F = + ' + ' Essential: wy', w, yz, 'yz' F = wy' + w + yz + =yz' z igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
33 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (a) F(,,,, E) = (,, 4, 5, 6, 7, 2, 25, 29 F = + E + m : ''''E' = m : ''''E = : '''E' = : '''E = : '''E' = : '''E = : ''E = 5 : ''E = 9 : 'E = '' = E E ''' = 'E E E igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
34 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (b) F(,,,, E) = ''E' + '''E' + ''' + '' + ' + ' F(,,,, E) = ''' + ''E' + '' + ' + ' ''E': 'E' + '''E' '''E': '''E' + ''''E' ''': '''E + '''E' + ''''E + ''''E' '': ''E + ''E' + '''E + '''E' ': 'E + 'E' + ''E + ''E' ': 'E + 'E' + ''E + ''E' ''' = ''E' '' E ' ' E = E E igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
35 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (a) w yz y w yz y m m m m w m 8 m 9 m m w m 8 m 9 m m (b) z F = (,, 2, 5, 8,, 3) F = 'z' + w''y' + w'y'z m m z F' = yz + z' + y + w'z F = (y' + z')(' + z)(' + y')(w' + + z') F = (, 3, 5, 7, 3, 5) F' = ' + ' F = ( + )( + ) F = '' + ' + ' m 8 m 9 m m (c) m m m 8 m 9 m m F = (, 3, 6, 9,, 2, 4) F' = ' + ' + ' F = ( + ')(' + ' + )(' + ' + ) F = + '' + ''' igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
36 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (a) F = y + z = ( + z )(y + z ) (b) m m m m m 8 m 9 m m m 8 m 9 m m F = ' + + ' + ' (c) m m F' '' + ' + ' F = ( + )( + ')(' + ' + ) m m m 8 m 9 m m m 8 m 9 m m F = ( + ' + ')(' + ' + ')(' + + ')(' + + ') F' = ' + + ' + ' F = ' + '' + ' + '' F' = + +' F = (' + ')( + ')(' + + ') igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
37 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (d) m m m m m 8 m 9 m m m 8 m 9 m m F =' + ' + F' = '' + '' + ' + ''' F = + ' + F = ( + )( + )(' + )( + + ) 3.4 m m m m m 8 m 9 m m m 8 m 9 m m SOP form (using s): POS form (using s): lternative POS: F = ''' + '' + ' + ' F = ''( + ') + (' + ') F' = ' + ' + '' + F = [(' + )( + ')][( + ' + )(' + ' + ')] F' = ' + ' + '' + '' F = [(' + )( + ')][( + ' + )(' + + )] igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
38 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (a) (b) m m yz m m y m 8 m 9 m m z F = F = '' + ' F = (,, 2, 3, 4, 5, 6, 7) F = (, 2, 6, 8,, 3, 4) (c) m m (d) m m m 8 m 9 m m m 8 m 9 m m F = ' + + F = '' + '' + F = (4, 5, 7, 2, 3, 4, 5) F = F = (,, 2, 3, 8,, 5) 3.6 (a) m m F = + '' F = ('('')')' m 8 m 9 m m ' ' ' F igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
39 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (b) m m F = + + ''' F = (()'()'(''' )')' m 8 m 9 m m ' ' ' ' F (c) m m m 8 m 9 m m F' = '' F = ('')' ' ' F (d) m m F = + F = (()' ()' )' F 3.7 igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
40 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ m m m m m 8 m 9 m m m 8 m 9 m m F = '' + '' + '' F' = + + F = ()'()'()' F' 3.8 F= ( )'( ) = (' + ')(' + ') = '' + '' + '' + '' m m m 8 m 9 m m ' ' ' ' F F = '' + '' + '' + '' and F' = '' + + '' + F = ('')'()'('')'()' = ( + )(' + ') (' + ')( + ) F' = [( + )(' + ')]' + [('+ ')( + )]' F = ([( + )(' + ')]' + [('+ ')( + )]')' F = ([( + )' + (' + ')'] + [('+ ')' + ( + )'])' igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
41 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ m m m 3.9 (a) F = (w + z )( + z )(w + + y ) yz y w 3 y z w m 8 m 9 m m w w z F z F = y'z' + w' + w'z' F =[(y + z)' + (w' + )' + (w + z)'] F' =[(y + z)' + (w' + )' + (w + z)']' (b) yz w m m y w' w m 8 m 9 m m w ' y' z' y z F z F = (, 2, 3, 4) F' = w' + w' + y'z' + yz = [(w +')(w' + )(y + z)(y' + z')]' F = (w +')' + (w' + )' + (y + z)' + (y' + z') (c) F = [( + y)(' + z)]' = ( + y)' + (' + z)' F' = [( + y)' + (' + z)']' y ' z F' 3.2 Multi-level NOR: F = (' + ')E + ( + ) F' = [(' + ')E + ( + )]' F' = [ [(' + ')' + E']' + [ ()' + ( + )']' ]' F' = [ [((' + )' + (' + )')' + E']' + [ (' + ')' + ( + )']' ]' igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
42 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ ' ' E' F ' ' Multi-level NN: F = (' + ')E + ( + ) F' = [ (' + ')E]' [( + )]' F' = [ ( (')'( ')' )'E]' [('')']' ' ' E F ' ' 3.2 F = w( + y + z) + yz F' = [w( + y + z)]'[yz]' = [w('y'z')')]'(yz)' y z ' y' z' w F igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
43 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ z y w 3.23 m m m 8 m 9 m m ' ' ' F 3.24 F = ' + '' + '' F' = + F = [ + ]' = [ + (' + ' + ']')]' m m m 8 m 9 m m (a) F = '' + ' + ' igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
44 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ F' = ('')'(')'(')' N-NN: ' ' ' ' F (b) F' = ['' + ' + ']' N-NOR: ' ' ' F ' (c) F = '' + ' + ' = ( + )' + (' + )' + (' + )' F' = ('')'(')'(')' = ( + )(' + )(' + ) F = [ ( + )(' + )(' + ) ]' OR-NN: ' ' (d) F = '' + ' + ' = ( + )' + (' + )' + (' + )' NOR-OR: ' ' F F N-N N OR-OR OR igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
45 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ ( )' ( )' N-NN NN OR-NOR NOR ('''')' [()' + (' ')]' NOR-NN OR NN-NOR N '' '' '''' ( )' ' + ' + ' + ' ( )' NOR-N NOR NN-OR NN The degenerate forms use 2-input gates to implement the functionality of 4-input gates ab cd f = abc' + c'd + a'cd'+ b'cd' c g = (a + b +c' + d')(b' + c' + d)(a'+ c + d') g' = a'b'cd + bcd' + ac'd c ab cd m m m m a m 8 m 9 m m b a m 8 m 9 m m b d fg = ac'd + abc'd + b'cd' d 3.27 y = 'y + y'; ual = (' + y)( + y') = ( y)' 3.28 y P y z z P (a) 3-bit odd parity generator (b) 4-bit odd parity generator igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
46 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ = E = ' + ' = ( ) F = ' + (' + ') = ' + ()' = () G = Half-dder S Half-dder S = E = ( ) F = () Half-dder S G = 3.3 F = '' + '' + '' + '' F = ( )' + ( ) ' = ( )( ) F 3.3 Note: It is assumed that a complemented input is generated by another circuit that is not part of the circuit that is to be described. (a) (b) module Fig_3_22a_gates (F,,,, _bar, ); output F; input,,, _bar, ; wire w, w2, w3, w4; and (w,, ); or (w2, w, ); and (w3, w2, ); and (w4,, _bar); or (F, w3, w4); module Fig_3_22b_gates (F,,,, _bar, ); output F; input,,, _bar, ; wire w, w2, w3, w4; not (w_bar, w); not (_bar, ); not (w3_bar, w3); not (w4_bar, w4); nand (w,, ); or (w2, w_bar, _bar); nand (w3, w2, ); nand (w4,, _bar); or (F, w3_bar, w4_bar); igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
47 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (c) (d) (e) (f) module Fig_3_23a_gates (F,, _bar,, _bar,, _bar); output F; input, _bar,, _bar,, _bar; wire w, w2, w3, w4; and (w,, _bar); and (w2, _bar, ); or (w3, w, w2); or (w4,, _bar); or (F, w3, w4); module Fig_3_23b_gates (F,, _bar,, _bar, _bar, ); output F; input, _bar,, _bar, _bar, ; wire w, w2, w3, w4; nand (w,, _bar); nand (w2, _bar, ); not (w_bar, w); not (w2_bar, w2); or (w3, w_bar, w2_bar); or (w4,, _bar); not (w5, _bar); not (w6, ); nand (F_bar, w5, w6); not (F, F_bar); module Fig_3_26_gates (F,,,,, E_bar); output F; input,,,, E_bar; wire w, w2, w_bar, w2_bar, w3_bar; not (w_bar, w); not (w2_bar, w2); not (w3_bar, E_bar); nor (w,, ); nor (w2,, ); nand (F, w_bar, w2_bar, w3_bar); module Fig_3_27_gates (F,, _bar,, _bar,, _bar); output F; input, _bar,, _bar,, _bar wire w, w2, w3, w4, w5, w6, w7, w8, w7_bar, w8_bar; not (w, _bar); not (w2, _bar); not (w3, ); not (w4, _bar); not (w7_bar, w7); not (w8_bar, w8); and (w5 w, w2); and (w6, w3, w4); nor (w7, w5, w6); nor (w8,, _bar); and (F, w7_bar, w8_bar); igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
48 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ Note: It is assumed that a complemented input is generated by another circuit that is not part of the circuit that is to be described. (a) (b) (c) (d) module Fig_3_22a_ (F,,,, _bar, ); output F; input,,, _bar, ; wire w, w2, w3, w4; assign w = & ; assign w2 = w ; assign w3 = w2 & ); assign w4 = & _bar); assign F = w3 w4); module Fig_3_22b_ (F,,,, _bar, ); output F; input,,, _bar, ; wire w, w2, w3, w4; assign w_bar = ~w; assign _bar = ~; assign w3_bar = ~w3; assign w4_bar = ~w4; assign w = ~( & ); assign w2 = w_bar _bar; assign w3 = ~(w2 & ); assign w4 = ~( & _bar); assign F = w3_bar w4_bar; module Fig_3_23a_ (F,, _bar,, _bar,, _bar); output F; input, _bar,, _bar,, _bar; wire w, w2, w3, w4; assign w = & _bar; assign w2 = _bar & ; assign w3 = w w2); assign w4 = _bar; assign F = w3 w4; module Fig_3_23b_ (F,, _bar,, _bar, _bar, ); output F; input, _bar,, _bar, _bar, ; wire w, w2, w3, w4; assign w = ~( & _bar); assign w2 = ~(_bar & ); assign w_bar = ~w; assign w2_bar = ~w2; assign w3 = w_bar w2_bar; assign w4, _bar; assign w5 = ~_bar; assign w6 = ~; assign F_bar = ~(w5 & w6); assign F = ~F_bar; igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
49 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (a) (e) (f) module Fig_3_26_ (F,,,,, E_bar); output F; input,,,, E_bar; wire w, w2, w_bar, w2_bar, w3_bar; not w_bar = ~w; not w2_bar = ~w2; not w3_bar = ~E_bar; nor w = ( ; nor w2 = ( ; nand F = ~( w_bar & w2_bar & w3_bar); module Fig_3_27_ (F,, _bar,, _bar,, _bar); output F; input, _bar,, _bar,, _bar wire w, w2, w3, w4, w5, w6, w7, w8, w7_bar, w8_bar; not w = ~_bar; not w2 = ~_bar; not w3 = ~; not w4 = ~_bar; not w7_bar = ~w7; not w8_bar = ~w8; assign w5 = w & w2; assign w6 = w3 & w4; assign w7 = ~(w5 w6); assign w8 = ~( _bar); assign F = w7_bar & w8_bar; w3 y w w w4 F = y Initially, with y =, w = w2 =, w3 = w4 = and F =. w should change to 4ns after y changes to. w4 should change to 8 ns after y changes to. F should change from to ns after w4 changes from to, i.e., 8 ns after y changes from to. (b) `timescale ns/ps module Prob_3_33 (output F, input, y); wire w, w2, w3, w4; and #8 (w3,, w); not #4 (w, ); and #8 (w4, y, w); not #4 (w2, y); or # (F, w3, w4); module t_prob_3_33 (); reg, y; wire F; igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
50 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ Prob_3_33 M (F,, y); initial #2 $finish; initial fork = ; y = ; #2 y = ; join (c) To simulate the circuit, it is assumed that the inputs y = have been applied sufficiently long for the circuit to be stable before y = is applied. The testbench sets y = at t = ns, and y = at t = ns. The simulator assumes that y = has been applied long enough for the circuit to be in a stable state at t = ns, and shows F = as the value of the output at t =. The waveforms show the response to y = applied at t = ns. Name.ns 39.29ns 78.58ns 7.87ns w y w2 w3 w4 F t = 28 ns t = 8 ns t = 4 ns t = ns = 8 ns Note: input change occurs at t = ns module Prob_3_34 (Out_, Out_2, Out_3,,,, ); output Out_, Out_2, Out_3; input,,, ; wire _bar, _bar, _bar, _bar; assign _bar = ~; assign _ar = ~; assign _bar = ~; assign _bar = ~; assign Out_ = ~( ( ) & (_bar ) & ); assign Out_2 = (( * _bar) ( & & ) (_bar & ) ) & ( _bar); assign Out_3 = & ( ( & ) ) ( & _bar); 3.35 module Empl-3(,,,, F) // Line inputs,,, Output, F, // Line 2 output // Line 3 and g(,, ); // Line 4 not (,, ), // Line 5 OR (F, ; ); // Line 6 igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
51 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ ofmodule; // Line 7 Line : ash not allowed, use underscore: Empl_3. Terminate line with semicolon (;). Line 2: inputs should be input (no s at the ). hange last comma (,) to semicolon (;). Output is declared but does not appear in the port list, and should be followed by a comma if it is inted to be in the list of inputs. If Output is a mispelling of output and is to declare output ports, should be followed by a semicolon (;) and F should be followed by a semicolon (;). Line 3: cannot be declared as input (Line 2) and output (Line 3). Terminate the line with a semicolon (;). Line 4: cannot be an output of the primitive if it is an input to the module Line 5: Too many entries for the not gate (only two allowed). Line 6: OR must be in lowercase: change to or. Line 7: is mispelled. Remove semicolon (no semicolon after ) (a) a d y z w F (b) w w6 w2 _lt_ w7 w3 _gt_ w4 _eq_ w5 (c) igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
52 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ a b y y UP_Majority_4 (y, a, b, c, d); outputy; input a, b, c, d; table // a b c d : y : ; : ; : ; : ; : ; : ; : ; : ; : ; : ; : ; : ; : ; : ; : ; : ; table primitive 3.38 module t_ircuit_with_up_2467; wire E, F; reg,,, ; ircuit_with_up_2467 m (E, F,,,, ); initial # $finish; initial fork = ; = ; = ; = ; #4 = ; #2 = ; #4 = ; #6 = ; # = ; #2 = ; #3 = ; #4 = ; #5 = ; #6 = ; #7 = ; #2 = ; join // Verilog model: User-defined Primitive primitive UP_2467 (,,, ); output ; input,, ; // Truth table for = f (,, ) = (, 2, 4, 6, 7); igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
53 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ table // : // olumn header comment : ; : ; : ; : ; : ; : ; : ; : ; table primitive // Verilog model: ircuit instantiation of ircuit_up_2467 module ircuit_with_up_2467 (e, f, a, b, c, d); output e, f; input a, b, c, d; UP_2467 M (e, a, b, c); and (f, e, d); //Option gate instance name omitted Name E F igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
54 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ HPTER 4 4. (a) T = ', T 2 = ', T 3 = + T = + ', T 4 = T 2 = (') = '' + ( + ') = '' + + ' F = T 3 + T 4 = + ' + '' + + ' With + = and + '' = + ': F = + ' + ' + ' lternative cover: F = + ' + ' + ' F 2 = T 2 + = ' + T T 2 T 3 T 4 F F 2 m m m 8 m 9 m m F = + '+ ' + ' m m m m m 8 m 9 m m m 8 m 9 m m F 2 = ' + F = + ' + ' + ' igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
55 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ ' [(')' ']'= + F (')' = + + ' G m m m m m F = ( + )(' + ) = ' + + += ' + F = ( + ')(' +) = '' + + ' = '' + 3 m 8 m 9 m m m 8 m 9 m m F = ' + + = ' + G = '' + + ' = '' (a) Y i = ( i S' + i S)E' for i =,, 2, 3 (b) 24 rows and 4 columns 4.4 (a) yz F yz y m m z F = 'y' + 'z' ' y' ' y' F igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
56 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ (b) 4.5 yz yz F yz yz m m z F = z m m y z = 'y + yz y ' y y z z F yz y m m y' y' z = 'y' + y'z + yz' z y yz y z' m m z z = 'z + z' 4.6 yz F yz m m y z F = z + yz + y z y z y F igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
57 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ module Prob_4_6 (output F, input, y, z); assign F = ( & z) (y & z) ( & y); 4.7 (a) wyz m m m 8 m 9 m m w = m m m 8 m 9 m m = ' + ' = m m m m m 8 m 9 m m m 8 m 9 m m y = '' '' + + '' = '( ) + ( )' = = X z = = y w y z (b) module Prob_4_7(output w,, y, z, input,,, ); (,,, ) case ({,,, }) 4'b: {w,, y, z} = 4'b; igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
58 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ 'b: 4'b: 4'b: 4'b: 4'b: 4'b: 4'b: 4'b: 4'b: 4'b: 4'b: 4'b: 4'b: 4'b: 4'b: case {w,, y, z} = 4'b; {w,, y, z} = 4'b; {w,, y, z} = 4'b; {w,, y, z} = 4'b; {w,, y, z} = 4'b; {w,, y, z} = 4'b; {w,, y, z} = 4'b; {w,, y, z} = 4'b; {w,, y, z} = 4'b; {w,, y, z} = 4'b; {w,, y, z} = 4'b; {w,, y, z} = 4'b; {w,, y, z} = 4'b; {w,, y, z} = 4'b; {w,, y, z} = 4'b; lternative model: module Prob_4_7(output w,, y, z, input,,, ); assign w = ; assign = ^ ); assign y = ^ ; assign z = y ^ ; 4.8 wyz m m m 8 m 9 m m m m m 8 m 9 m m m m m 8 m 9 m m w = +'' = ' + ' +'' y = ' +' z = igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
59 27 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This publication is protected by opyright and written permission should be obtained or likewise. For information regarding permission(s), write to: Rights and Permissions epartment, Pearson Education, Inc., Upper Saddle River, NJ lternative model: module Prob_4_8(output w,, y, z, input,,, ); assign w = (&) ( & (~)) & (~) ; assign = ( (~) & ) ((~) & ) ( & (~)) & (~); assign y = ^ ; assign z = ; 4.9 a b c d e f g m m m 8 m 9 m m m m m 8 m 9 m m a = ' + ' + ''' + '' b = '' + ''' + ' + '' m m m m m 8 m 9 m m m 8 m 9 m m c = ' + ' + ''' + '' d = '' + '' + ''' + '' + '' m m m 3 m m m m m 3 m 8 m 9 m m m 8 m 9 m m m 8 m 9 m m e = '' + ''' f = '' + ''' + ' + '' g = '' + '' + '' + '' igital esign Solution Manual. M. Mano. M.. iletti, opyright 27, ll rights reserved.
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