Simplify the following Boolean function:

f (A, B,C) = ABC + ABC + ABC + ABC

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UPSC ESE Electronics & Communication 2022 Official Paper
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  1. ABC + ABC + AB
  2. ABC + AC + AB
  3. AB + BC + AC
  4. ABC + AC + AB

Answer (Detailed Solution Below)

Option 3 : AB + BC + AC
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Detailed Solution

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f (A, B,C) = ABC + ABC + ABC + ABC

 A¯BC+AB¯C+AB(C+C¯)

The above equation can also be written as :

A¯BC(A+A¯)+AB¯C(B+B¯)+ABC+ABC¯

0+BC+AC+0+AB(C+C¯)

BC+AC+AB

 

Hence option 3 is correct

Formulae:

  1. A + 1 = 1
  2. A + 0 = A
  3. A . 1 = A
  4. A . 0 = 0
  5. A + A = A
  6. A . A = A
  7. A¯ = A
  8. A + A¯ = 1
  9. A . A¯ = 0
  10. A+B = B+A
  11. A.B = B.A
  12. A+B = A¯.B¯
  13. A.B = A¯+B¯
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