Computer Science – 15.2 Boolean Algebra and Logic Circuits | e-Consult
15.2 Boolean Algebra and Logic Circuits (1 questions)
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Answer:
The Boolean expression is R = (P + Q) * (~P * Q). We can use a 2-variable Karnaugh map to simplify this.
| 00 | 01 | 11 | 10 |
| 01 | 11 | 10 | 00 |
The expression (P + Q) * (~P * Q) can be rewritten as P + Q * (~P * Q). This can be simplified by noticing that Q * (~P * Q) = Q * (~P) * Q = ~P * Q2 = ~P * Q. Therefore, the expression becomes P + ~P * Q.
Now, we can group the '1's in the Karnaugh map:
- The '1's in the first row (00 and 01) can be grouped.
- The '1's in the third column (11 and 10) can be grouped.
This gives us the simplified expression: R = P + Q