CSE140 Exercise on April 16, 2009
(I) (Laws and Theorems of Boolean Algebra) Prove using Boolean algebra that
a′c′+ab +ac +a′b′=a′c′+ab +b′c.Write the particular lawyou are using in each
step.
(II) (Laws and Theorems of Boolean Algebra) Prove using Boolean algebra that
(a+c)(a′+c′)(b′+c+d′)(a+b′+d′)=(a+c)(a′+c′)(b′+d′). Write the particular law
you are using in each step.
(III) (Karnaugh Map) Use Karnaugh map to simplify function
f(a,b,c,d)=Σm(0,1,2,3,4,5,7,8,12) +Σd(1 0,11).List all possible minimal two-level
sum of products expressions. Showthe switching functions. No need for the diagram.
(IV) (Karnaugh Map) Use Karnaugh map to simplify function
f(a,b,c,d)=Σm(0,1,2,3,4,5,7,8,12) +Σd(1 0,11).List all possible minimal two-level
product of sums expressions. Showthe switching functions. No need for the diagram.
(V) Universal Set of Gates: Check if the set in the following list is universal and explain
your decision. Assuming constants 0 and 1 are available as inputs.
i. {AND, NOT}
ii. {NAND}
iii. {XOR, NOT}
iv.{f(x,y)}, where f(x,y)=x′y
v. {g(x,y,z)}, where g(x,y,z)=(x+y)z′
vi. { f(x,y), g(x,y)}, where f(x,y)=x′y+xy′and g(x,y)=x′y′
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