1. 3.3 Simplify the following Boolean expression using three-variable maps:
d) F(x, y, z) = x y z + x\ y\ z + x y\ z\ y yz 00 01 11 10 1 x x z
x y z
x y\ z \
x\ y\ z

2. 3.5 Simplify the following Boolean expression using four-variable maps: a) F(w,x, y, z) = (1,4,5,6,12,14,15) y yz 00 01 11 10 1 wx
w\ y\ z
w x y
x z\ x w z
F =w\ y\ z+w x y+ x z\

3. 3.5 Simplify the following Boolean expression using four-variable maps: b) F(A,B,C,D)= (1,5,9,10,11,14,15) C CD 00 01 11 10 1
A\ C\ D AB
A C
A B\ D B
B\ C\ D A D
F =A\C\D+AC+(AB\D or B\C\D)

4. 3.5 Simplify the following Boolean expression using four-variable maps: c) F(w,x, y, z) = (0,1,4,5,6,7,8,9) y yz 00 01 11 10 1
x\ y\ wx
w\ x x w z
F =x\y\+w\x

5. 3.5 Simplify the following Boolean expression using four-variable maps: d) F(A,B,C,D)= (0,2,4,5,6,7,8,10,13,15) C CD 00 01 11 10 1
B\ D\ AB
B D
A\ B B
A\ D\ A D
F =B\D\+BD+(A\B or A\D\)

6. 3.6 Simplify the following Boolean expression using four-variable maps: a)A\B\C\D\+AC\D\+B\CD\+A\BCD+BC\D C CD 00 01 11 10 1
B\ D\ AB
A\ B D
A B C\ B A D
F =B\D\+A\BD+ABC\

7. 3.6 Simplify the following Boolean expression using four-variable maps: b) x\z+w\xy\+w(x\y+xy\)
= x\z+w\xy\+wx\y+wxy\ y yz 00 01 11 10 1
x\ z wx
x y\
w x\ y x w z
F =x\ z+xy\+wx\y

8. 3.6 Simplify the following Boolean expression using four-variable maps: c)A\B\C\D\+A\CD\+AB\D\+ABCD+A\BD C CD 00 01 11 10 1
B\ D\ AB
A\ B D
B C D B
A\ B C
A\ C D\ A D
F =B\D\+A\BD+BCD+(A\BC or A\CD\)

9. 3.6 Simplify the following Boolean expression using four-variable maps: d)A\B\C\D\+AB\C+B\CD\+ABCD\+BC\D C CD 00 01 11 10 1
A\ B\ D\ AB
B C\ D
A C D\ B
A B\ C A D
F =A\B\D\+BC\D+ACD\+AB\C

10. 3.10 Simplify the following Boolean function by first finding the essential prime implicants:c) F(A,B,C,D)=(1,3,4,5,10,11,12,13,14,15) C CD 00 01 11 10 1
B C\ essential AB
A C essential
A\ B\ D essential B
A B non-essential A
A\ C\ D non-essential
B\ C D non-essential
Redundant D
F =BC\+AC+A\B\D

11. 3.13 Simplify the following Boolean expression to (1) sum-of-products (2) product-of-sums b) ACD\+C\D+AB\+ABCD 1) C CD 00 01 11 10 1
C\ D AB
A C
A B\ B A D
F = C\D+AC+AB\

12. 3.13 Simplify the following Boolean expression to (1) sum-of-products (2) product-of-sums b) ACD\+C\D+AB\+ABCD 2) C CD 00 01 11 10 1
A\ D\ AB
A\ C
B C\ D\ B A
F\ = A\D\+A\C+BC\D\ D
F = (A+D)(A+C\)(B\+C+D)