Math Problem Statement

If input B is provided to a NOT gate, what will be the output?

Solution

The image you've shared shows a logical circuit involving a NOT gate. The NOT gate inverts the input value, meaning:

  • If the input (denoted as BB) is true, the output will be false.
  • If the input BB is false, the output will be true.

Looking at the answer options:

  1. The output will be true no matter what the value of input B is.
    This is incorrect because the output depends on the value of BB.

  2. The output will be false no matter what the value of input B is.
    This is incorrect for the same reason as above.

  3. If B is true, then output will be true. If B is false, then output will be false.
    This is incorrect because it describes a direct relationship (not inversion).

  4. If B is true, then output will be false. If B is false, then output will be true.
    This is correct because it correctly represents the behavior of the NOT gate.

Therefore, the correct answer is:
"If B is true, then output will be false. If B is false, then output will be true."

Would you like a further breakdown of how logic gates work?

Here are 5 questions that might interest you:

  1. What is the difference between AND, OR, and NOT gates?
  2. How can multiple logic gates be combined to form more complex circuits?
  3. What is the truth table for a NOT gate?
  4. How do XOR gates work and how are they different from OR gates?
  5. Can you explain De Morgan's Laws in logic?

Tip: When studying logic gates, practicing with truth tables can help visualize how different inputs affect outputs.

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Math Problem Analysis

Mathematical Concepts

Boolean Algebra
Logic Gates

Formulas

NOT Gate Formula: output = NOT(input)
Truth Table for NOT Gate

Theorems

Inversion Theorem
Basic Boolean Theorems

Suitable Grade Level

Grades 9-12