Question

1) The Boolean function: F = AB + CD can be implemented by using one 3-to-8 decoder and one OR gate (any other external logic gates cannot be used). True or False.

2) What is the arithmetic equivalence for a shift right operation? 1) Half the value 2) Double the value 3) Add by two 4) Minus by two

3) What is the simplification result for Boolean expression: A(A+B) + A' + C

Answer 1

1) The Boolean function: F = AB + CD can be implemented by using one 3-to-8 decoder and one OR gate (any

other external logic gates cannot be used).

Answer: False.

Because we need two AND gates also inorder to implement Boolean function: F = AB + CD

2) What is the arithmetic equivalence for a shift right operation?

Answer: Option 3) Add by two

3) What is the simplification result for Boolean expression: A(A+B) + A' + C

Answer:

Given Boolean expression is F= A(A+B) + A' + C

   F= AA+AB + A' + C { By Distributive Law A(B+C)= AB + AC }

   F= A+ AB + A' + C { We know that By Identity Law A.A=A}

F= ( A + A' ) + AB + C { We know that A + A' = 1 }

F= ( 1 ) + C + AB

      F=1 + AB { By boolean postulates 1+C = 1 }

F= ( 1 + A) . ( 1 + B ) { By Distributive Law A+BC= ( A + B ) + ( A + C )}

The Required simplification result for Boolean expression is F= ( 1 + A) . ( 1 + B )