SOLUTIONSMANUAL - LIZY KURIAN JOHN  NOTE: (For Complete File, ...

SOLUTIONS MANUAL 

TO ACCOMPANY 

DIGITAL SYSTEMS 

DESIGN 

USING VHDL

®   Third Edition 

CHARLES H. ROTH, JR. 

LIZY KURIAN JOHN 

NOTE: (For Complete File, Download link at the end of this File) 1 / 4

1 © 2018 Cengage Learning®. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.Chapter 1 Solutions

1.1

A  B  C  A

⊕ B B ' ⊕ C (A ⊕ B) · C A ' · (B' ⊕ C) F 

0 0 0 0 1 0 1 1

0 0 1 0 0 0 0 0

0 1 0 1 0 0 0 0

0 1 1 1 1 1 1 1

1 0 0 1 1 0 0 0

1 0 1 1 0 1 0 1

1 1 0 0 0 0 0 0

1 1 1 0 1 0 0 0

1.2

X  Y  B

in Diff  B out

0 0 0 0 0

0 0 1 1 1

0 1 0 1 1

0 1 1 0 1

1 0 0 1 0

1 0 1 0 0

1 1 0 0 0

1 1 1 1 1

Sum of Products: Diff = XY 

'Bin' + X 'Y 'Bin + XYB in + X 'YBin' B out = X 'Bin + X 'Y + YB in

Product of Sums: Diff = (X + Y + B

in)(X + Y ' + Bin')(X ' + Y + B in')(X ' + Y ' +Bin) B out = (Y + B in)(X ' + Bin)(X ' + Y)

1.3    uclCd55Cid67c1lc.c2C8d. d95c4ClSCeClSC0clC u 0=B’D. Set E, F’, G, and H, to 1 one at a time and all 1’s to X’s to get MS

1=C’D(E), MS2=ABC(F’), MS3=BC’D’(G + H)

Z = B

'D + C 'DE + ABCF  ' + BC 'D'G + BC 'D'H '

1.4 (a) F = A

'D' + AC 'D + BCD' + A'B'C 'E + BD'E

(b) Z = A

'CD' + C 'D + BC 'E + B'DE + CD 'F + A'C 'G

(c) H = A 'CD + A 'B'CE + BCDF' (d) G = C 

'E 'F + DEF + AD 'F '

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2 © 2018 Cengage Learning®. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

1.5

-C4ldl 3Cr7/d0d.2CS33o.4C1/c1CA = 0, D = 0, and C changes. When C changes from 1 to 0; A 'C also goes from 1 to 0. The hazard occurs because C  ' hasn’t become 1 yet since it has to go through the inverter; therefore, F goes to 0 momentarily before going to 1 . Gate delays are assumed to be 10ns in the timing diagram below.

1.6

F = bc ' + b'd' + a'cd'

3 hazards: A=0, C=0, D=0, B changes

A=1, C=0, D=0, B changes A=0, B=1, D=0, C changes

To eliminate the hazards, add the term c'd' (combining the four 1’s in the top row) and replace a 'cd' with a 'd' (combining two 1’s from the bottom left with two 1’s from the top left.)

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3 © 2018 Cengage Learning®. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.

1.7 (a)

F = ((ab)’.(a+c)’+(a’+d)’)’ = ab + ((a+c)’+(a’+d)’)’ = ab + (a + c)(a ' + d) = ab + aa ' + ad + a 'c + cd; + .35cCd55Cl/c4cClc.i4CS1Cl/cC67id63Cd.3C4/S14C1cd.by1’s not in the same product term, indicating a 1 hazard.r7/d0d.2Cbcd = 110, a changing 1 => 0 gates 1,5,3,4,5,

• => 1 gates 3,4,5,1,5

F = ab + aa ' + ad + a 'c + cd = ab + a(a ' + d) + c(a ' + d)  = ab + (a+c) (a ' + d) = (ab + a +c)(ab + a ' +dpC 774ccC4d95cCr7rCnS.C!SS5cd1C5d14C = (a + c)(a + a' + d)(a' + b + dpCC77Cdbd9)d3Cd"b2bd9)ad"b2bdpad"b2b9pC + .35cCd55Cl/c4cClc.i4CSnCe"4C 1Cl/cC67id63Cd.3C4/Sws 0’s not in same term.

e7/d0d.2Cbcd = 000, a changing 0 => 1 gates 3,4,5,3,5

• => 0 gates 3,4,5,2,5

(b) 2cC1 55C2c4 01CdC,75c8c5C4oiCSnC6.S2o3l4C3 .3o lC9c3do4cCdC,75c8c5C4oi7Sn76.S2o3l4C3 .3o lC/d4C 1SCe7/d0d.2Cd4C5S10Cd4Cd1C 16olCd12C l4C3Si65cic1lCare not connected to the same AND gate.-8S 2Cr7/d0d.2C95Cd22 10C6.S2o3lClc.iC93$C;4cC:-:#Cgates as asked in the question. 

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