Which are the essential prime implicants of the following Boolean function? f…
2004
Which are the essential prime implicants of the following Boolean function?
f (a, b, c) = a’c + ac’ + b’c
Answer: A. a’c and ac’ — Identify Prime Implicants (Groups) Group 1 (m1, m3): Corresponds to a′c. Analysis: Minterm 3 is only covered by this group. Therefore, this is an Essential…
- A.
a’c and ac’
- B.
a’c and b’c
- C.
a’c only
- D.
ac’ and bc’
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Correct answer: A
Identify Prime Implicants (Groups)
Group 1 (m1, m3): Corresponds to a′c.
Analysis: Minterm 3 is only covered by this group. Therefore, this is an Essential Prime Implicant.
Group 2 (m4, m6): Corresponds to ac′.
Analysis: Minterm 6 is only covered by this group. Therefore, this is an Essential Prime Implicant.
Other Groups: Groups can be formed for (m1,m5) and (m4,m5), but m5 is not unique to a single prime implicant (it can be covered by either b′c or ab′), so these are not essential.
Conclusion The Essential Prime Implicants are a′c and ac′.
Correct Option: (A)
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