1. P.50
1.1)
a) To Hexa
4* + 3X + 7* + 5* =
287.625/16 F
17/16 1
1/16 1
0
=
b) (B8E.F) To Octal

=
2958/8 6
369/8 1
46/8 6
5/8 5
0
=
C)
=
6/8 6
0
=

2. P.109
2.2)
a) X’Y’ + X’Y + XY = X’ + Y
X’(Y’ + Y) + XY
(X’ + X) + (X’ + Y) = X’ + Y
b) A’B + B’C’ + AB + B’C = 1
B(A’ + A) + B’(C’ + C)
= B + B’ = 1
c) Y + X’Z + XY’ = X + Y + Z
(Y + Y’) + (Y + X) + X’Z
Y + X + X’Z
Y + (X + X’) + (X + Z)
= Y + X + Z
D)
X’Y’ + Y’Z + XZ + XY + YZ = X’Y’ + XZ + YZ’
Z(Y’ + Y) + X’Y’ + XZ + XY
Z + X’Y’ + XZ + XY
= X’Y’ + XZ + YZ’

3. P.111
2.14)
a) F(A,B,C) = ∑
B’ B
A’ 1 0 1 1
A 1 0 0 0
C’ C C’
F = B’C’ + A’B
b) F(X,Y,Z) = ∑
F = X’Z + XY’
c) F(P,Q,R) = ∑
F = P’R + PR’
d) F(A,B,C) = ∑
B’ B
A’ 1 1 1 0
A 1 0 0 0
C’ C C’
F = B’C’ + A’C
Y’ Y
X’ 0 1 1 0
X 1 1 0 0
Z’ Z Z’
Q’ Q
P’ 0 1 1 0
P 1 0 0 1
R’ R R’

4. 2.15)
a) ACD’ + BC + ABCD’ + AB’C
C’ C
A’ 0 0 0 0 B’
0 0 1 1 B
A 0 0 1 1
0 0 1 1 B’
D’ D D’
 ∑
 F = AC + BC
b) ABC’D + ACD’ + AB’C + C’D
C’ C
A’ 1 0 0 0 B’
1 0 0 0 B
A 1 1 0 1
1 0 1 1 B’
D’ D D’
 ∑
 F = C’D’ + AC’B + D’CA + AD’C
c) ABC’D + ACD’ + AB’C + C’D
C’ C
A’ 0 1 1 0 B’
0 0 1 1 B
A 0 0 0 0
0 1 0 0 B’
D’ D D’
 ∑
 F = A’BC + A’B’D + B’C’D

5. P.112
2.18)
a) XY’ + XZ’ + XYZ
Y’ Y
X' 0 0 0 0
X 1 1 1 1
Z’ Z Z’
 ∑
 F = X
b) XYZ’ + WX’Y + WXY’ + W’X’Y + WXYZ
Y’ Y
W’ 0 0 1 1 X’
0 0 0 1
X
W 1 1 1 1
0 0 1 1 X’
Z’ Z Z’
 ∑
 F = YZ’ + WX + W’X’Y + WX’Y
c) BD + AB’D + AB’C
Y’ Y
A’ 0 0 1 1 B’
0 0 0 1
B
A 1 1 1 1
0 0 1 1 B’
D’ D D’
 ∑
 F = ACB’ + BD + AD

6. p.113
2.24)
a) F(A,B,C,D) = ∑ , J(A,B,C,D) = ∑
Y’ Y
A’ 1 1 0 X B’
0 0 1 X
B
A 0 1 1 0
X X 0 X B’
D’ D D’
ANSWER IS: A’B’C + ABD + BCD
b) F(A,B,C,D) = ∑ , J(A,B,C,D) = ∑
C’ C
A’ 0 0 X 1 B’
1 X 0 X
B
A 1 X 1 0
0 1 0 0 B’
D’ D D’
ANSWER IS: BC’ + ADC’ + ABD + A’B’C
c) F(A,B,C) = ∑ , J(A,B,C) = ∑
B’ B
A' X 1 X 1
A 1 0 X X
C’ C C’
ANSWER IS: A’ + C’

7. p.113
2.25)
a) F(A,B,C) = ∑ , J(A,B,C) = ∑
B’ B
A' X 0 1 0
A 0 1 X 1
C’ C C’
ANSWER IS: AB + AC + BC’
b) F(W,X,Y,Z) = ∑ , J(W,X,Y,Z) = ∑
Y’ Y
W’ 1 0 0 1 X’
1 1 X 0
X
W 0 X 1 1
1 0 X 0 X’
Z’ Z Z’
ANSWER IS: W’Y’Z’ + X’Y’Z’ + XZ + WXY + W’X’YZ’
c) F(A,B,C,D) = ∑ , J(A,B,C,D) = ∑
C’ C
A’ 0 0 X X B’
1 X 1 1
B
A 1 0 1 X
1 0 X X B’
D’ D D’
ANSWER IS: C + A’B + AC’D’

8. p.111
2.12)
a) (A’B’ + C)(B + CD)
A B C D A’ B’ A’B’ CD A’B’ + C B’ + CD F
0 0 0 0 1 1 1 0 1 1 1
0 0 0 1 1 1 1 0 1 1 1
0 0 1 0 1 1 1 0 1 1 1
0 0 1 1 1 1 1 1 1 1 1
0 1 0 0 1 0 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0
0 1 1 0 1 0 0 0 1 0 0
0 1 1 1 1 0 0 1 1 1 1
1 0 0 0 0 1 0 0 0 1 0
1 0 0 1 0 1 0 0 0 1 0
1 0 1 0 0 1 0 0 1 1 1
1 0 1 1 0 1 0 1 1 1 1
1 1 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 0 0 0 0
1 1 1 0 0 0 0 0 1 0 0
1 1 1 1 0 0 0 1 1 1 1
 Sum Of Product Is: F = M0 + M2 + M3 + M7 + M10 + M11 + M15
A’B’C’D’ + A’B’C’D + A’B’CD’ + A’BCD + A’BCD + AB’CD’ + AB’CD + ABCD
 Product Of Sum Is: F = M4 + M5 + M6 + M8 + M9 + M12 + M13 + M14
(A’ + B + C’ + D’).(A’ + B + C’ + D).(A’ + B + C + D’).(A + B’ + C’ + D’).(A + B’ + C’ + D).(A + B
+ C’ + D’).(A + B + C’ + D).(A + B + C + D’)

9. b) X(X + Y’)(Y’Z’)
x y Z X’ Y’ Z’ X + Y’ Y’Z X(X + Y’)(Y’Z’) F
0 0 0 1 1 1 1 1 0 1
0 0 1 1 1 0 1 0 0 1
0 1 0 1 0 1 0 0 0 1
0 1 1 1 0 0 0 0 0 1
1 0 0 0 1 1 1 1 1 1
1 0 1 0 1 0 1 0 0 0
1 1 0 0 0 1 1 0 0 0
1 1 1 0 0 0 1 0 0 0
 Sum Of Product Is: F = M0 + M1 + M2 + M3 + M4
X’Y’Z’ + X’Y’Z + X’YZ’ + X’YZ + XY’Z’
 Product Of Sum Is: F = M5 + M6 + M7
(X’ + Y + Z’).(X’ + Y’ + Z).(X’ + Y’ + Z’)

10. 2.12)
a) (A’B’ + C)(B + CD)
A B C D B’ C’ D’ AB’ CD’ AC’D ABCD F
0 0 0 0 1 1 1 0 0 0 0 0
0 0 0 1 1 1 0 0 0 0 0 0
0 0 1 0 1 0 1 0 1 0 0 1
0 0 1 1 1 0 0 0 0 0 0 0
0 1 0 0 0 1 1 0 0 0 0 0
0 1 0 1 0 1 0 0 0 0 0 0
0 1 1 0 0 0 1 0 1 0 0 1
0 1 1 1 0 0 0 0 0 0 0 0
1 0 0 0 1 1 1 1 0 0 0 1
1 0 0 1 1 1 0 1 0 1 0 1
1 0 1 0 1 0 1 1 1 0 0 1
1 0 1 1 1 0 0 1 0 0 0 1
1 1 0 0 0 1 1 0 0 0 0 0
1 1 0 1 0 1 0 0 0 1 0 1
1 1 1 0 0 0 1 0 1 0 0 1
1 1 1 1 0 0 0 0 0 0 1 1
 Sum Of Product Is: F = M2 + M6 + M8 + M9 + M10 + M11 + M13 + M14 + M15
A’B’CD + A’BCD’ + A’B’CD’ + AB’C’D’ + AB’C’D + AB’CD’ + AB’CD + ABC’D + ABCD’ + ABCD
 Product Of Sum Is: F = M0 + M1 + M3 + M4 + M5 + M7 + M12
(A’ + B’ + C’ + D’).(A’ + B’ + C’ + D).(A’ + B’ + C + D).(A’ + B + C’ + D’).(A’ + B + C’ + D).(A’ +
B + C + D).(A + B + C’ + D’)