Boolean Function

Question

The given logic circuit is realizing the function f(A,B,C,D) = $\Sigma$(1,4,5,8,10,12,14,15) and function f2 is f(A,B,C,D) = A'B + AB' + AC'D Identify the value of f3 ?

 

 

 

 

A. 

B. 

C. 

D. 

 

Comments

change the don't care terms for option D

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CASE :  ABCD = 15  = m₁₅ = 1 

Don't care means where Its 0 or 1 it's doesn't reflect any changes to our output

but if f3 = 1  then F  = 0  (which is not correct )

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Answer is given as C

Answer 1

Answer C option

Function f2 = A'B+AB'+ AC'D

 F2 = SOP ( 4,5,6,7,8,9,10,11,13)

  then Function F1 should be SOP (4,5,8,10)

	A'B'	A'B	AB	AB'
C'D'		1		1
C'D		1	1	1
CD		1		1
CD'		1		1

Option C 

F3 :∏(1,12,14,15) * d(4,5,8,10)  compliment is  F3: ∏(0,2,3,6,7,9,11,13)* d(4,5,8,10) it represents POS

then SOP will F3 can be represent in this form ∑(1,12,14,15) + d(4,5,8,10)

	A'B'	A'B	AB	AB'
C'D'		d	1	d
C'D	1	d
CD			1
CD'			1	d

(F1 AND F2) OR F3' = ∑(1,4,5,8,10,12,14,15)

(((4,5,8,10) ⋂ ( 4,5,6,7,8,9,10,11,13)) ⋃ (1,12,14,15)+d(4,5,8,10))

= (1,4,5,8,10,12,14,15).

 

Comments

then Function F1 should be SOP (4,5,8,10)

why this restriction?

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To get the output ,we have to manage F1