onstruct a truth table for the following boolean expressions of ABC + NOT A NOT B NOT C
Question
Solution
Sure, here is the truth table for the boolean expression ABC + NOT A NOT B NOT C:
| A | B | C | ABC | NOT A | NOT B | NOT C | NOT A NOT B NOT C | ABC + NOT A NOT B NOT C |
|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |
| 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 |
| 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 |
Here's how to read the table:
- The first three columns (A, B, C) represent all possible combinations of truth values for A, B, and C.
- The next column (ABC) represents the AND operation on A, B, and C.
- The next three columns (NOT A, NOT B, NOT C) represent the negation of A, B, and C respectively.
- The next column (NOT A NOT B NOT C) represents the AND operation on NOT A, NOT B, and NOT C.
- The final column (ABC + NOT A NOT B NOT C) represents the OR operation on ABC and NOT A NOT B NOT C.
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