Simplifying Boolean Expression A + AB
We need to simplify the given Boolean expression:
$ A + AB $
Applying Boolean Algebra Rule
This expression can be simplified using the Absorption Law in Boolean algebra. The Absorption Law states that for any Boolean variables X and Y:
$ X + XY = X $
Step-by-Step Simplification
Let's apply this law to our expression $ A + AB $.
- Identify $ X $ and $ Y $ in the expression $ A + AB $. Here, $ X = A $ and $ Y = B $.
- Apply the Absorption Law formula $ X + XY = X $.
- Substituting $ X = A $ and $ Y = B $ into the formula, we get: $ A + AB = A $.
Alternatively, we can factor out A:
$ A + AB = A(1 + B) $
Using the Identity Rule ($ 1 + B = 1 $):
$ A(1) = A $
Final Result
Both methods confirm that the simplified form of the Boolean expression $ A + AB $ is $ A $.
Options Review
Comparing this result with the given options:
- Option 1: B
- Option 2: A+1
- Option 3: AB
- Option 4: A (This matches our result)
Important Questions from Digital Electronics
Latches are _______ circuits.
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Which of the following is a non-positional number system?
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