Which of the following is the simplified form of the given function.

f(A, B, C) = ∑m(0, 1, 3, 7)

The correct answer is A'B' + BC.

Key Points

• To simplify the given function f(A, B, C) = Σm(0, 1, 3, 7), we use the Karnaugh map method.
• We place the minterms in the Karnaugh map:
  • m(0): A'B'C'
  • m(1): A'B'C
  • m(3): A'BC
  • m(7): ABC
• Grouping the 1s in the Karnaugh map:
  • Group 1: A'B' (covers m(0) and m(1))
  • Group 2: BC (covers m(3) and m(7))
• Therefore, the simplified form is A'B' + BC.

Additional Information

• The simplification process helps to reduce the complexity of the Boolean function, making it easier to implement in digital circuits.
• The Karnaugh map is a visual method used to simplify Boolean expressions without using Boolean algebra theorems and properties.
• Minimizing Boolean functions is essential in designing efficient digital systems with fewer gates and reduced power consumption.