Question
Download Solution PDFWhich of the following is the simplified form of the given function.
f(A, B, C) = ∑m(0, 1, 3, 7)
Answer (Detailed Solution Below)
Option 3 : A'B' + BC
Detailed Solution
Download Solution PDFThe 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.