in Digital Logic edited by
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14 votes
14 votes

The minimum Boolean expression for the following circuit is

  1. $\text{AB + AC + BC}$
  2. $\text{A + BC}$
  3. $\text{A + B}$
  4. $\text{A + B + C}$
in Digital Logic edited by
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if $a,b$ switches are in series connection then it can be written as $a.b$

if $a,b$ switches are in parallel connection then it can be written as $a+b$

so from the given circuit:

$\implies A.(B+C)+A.B+(A+B).C$

$\implies AB+AC+AB+AC+BC$

$\implies AB+BC+AC$
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2 Answers

23 votes
23 votes
Best answer

A(B+C) + AB + (A+B)C

=AB+AC+AB+AC+BC

=AB+AC+BC 

Hence,Option(A)AB+AC+BC.

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Hi
how you are determining whether (a+b) or ab. can you please provide me a source to learn this concept. Bit confusing, confused during my b.tech too :-P
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@LeenSharma In the lowest portion of the circuit diagram AB should be (A+B) & AB+C should be (A+B)C
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7 votes
7 votes

2 switch a,b in series =a.b

2 switch a,b in parallel=a+b 

so above circuit diagram gives expression A(B+C)+AB+(A+B)C

=AB+AC+AB+AC+BC=AB+AC+BC  Option A is Correct

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please correct the word gives
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