Learning Objectives
  • Define the function of a NOT gate.
  • Complete the two-row truth table for NOT.
  • Trace NOT gates in larger circuits.
  • Use NOT correctly in expressions and problem statements.
Key Terms
NOT gate
A single-input gate that produces the opposite Boolean value.
Inversion
Changing 0 to 1 or changing 1 to 0.
Complement
The opposite Boolean value of a variable.
Input
The single value entering the NOT gate.
Output
The inverted value leaving the NOT gate.
NOT A
A logic expression meaning the opposite of A.
Summary diagram
Summary Of The Main Ideas In This Lesson
Function Of NOT

The NOT gate reverses its input. If the input is 0, the output is 1. If the input is 1, the output is 0. Because there are only two possible input values, the NOT truth table has two rows.

NOT is the only required gate with one input. Its symbol is a triangle followed by a small output bubble. The bubble indicates inversion.

The result can be written as NOT A. Some sources use a bar or other Boolean notation, but word-based expressions such as NOT A are clear and match the gate name.

Truth Table For NOT
A X = NOT A
0 1
1 0
Using NOT In A Problem Statement

A NOT operation is required when an output depends on the absence or opposite of a condition. If input D is 1 when daylight is detected, a lamp that turns on when daylight is not detected may use X = NOT D.

Always check how the input is defined. If D were instead defined as 1 when it is dark, the same lamp could be controlled directly by D and no NOT gate would be needed.

Words such as not, no, closed when the input represents open, or inactive when the input represents active often signal inversion.

NOT In A Multi-Gate Circuit

When a NOT gate feeds another gate, calculate the NOT output first. For X = (NOT A) AND B, make a column for NOT A before applying AND with B.

If A = 0 and B = 1, NOT A = 1, so X = 1 AND 1 = 1. If A = 1 and B = 1, NOT A = 0, so X = 0.

Writing the intermediate column prevents the common mistake of applying NOT to the final output instead of only to A.

Placement Of NOT Matters

NOT can apply to one variable or to the result of a whole gate. These are different structures. NOT A AND B means invert A first and then AND with B. NOT (A AND B) means apply AND first and invert the combined result, which is a NAND operation.

Brackets and circuit connections show the intended scope. In a circuit, follow the wire entering the NOT symbol. In an expression, identify the exact variable or bracket after NOT.

Do not move a NOT gate to another part of a circuit. The syllabus requires the given structure to be preserved rather than simplified or transformed.

Double Inversion

Two NOT gates in sequence return the original value: 0 becomes 1 then 0, and 1 becomes 0 then 1. This observation can help when tracing a given circuit.

However, if a question asks you to draw the circuit from an expression containing two NOT operations, draw both gates because circuits must not be simplified. The aim is to represent the supplied statement exactly.

Common Contexts

A NOT gate can represent a warning when a safety condition is not met, a light when daylight is not present, or a pump when a full-level sensor is not active.

These contexts are only ways of describing the same rule. The exam answer should connect the wording to the binary definition and then apply the NOT truth table.

Worked Examples
Tracing A NOT Gate

Question: Input A is 1. What is X if X = NOT A?

  1. Read A = 1.
  2. Reverse the value.

Answer: X = 0.

NOT Before AND

Question: Find X for A = 0 and B = 1 when X = (NOT A) AND B.

  1. NOT A = 1.
  2. Apply AND to 1 and B = 1.
  3. AND outputs 1 because both inputs are 1.

Answer: X = 1.

Examination Guidance
  • Remember that the NOT truth table has only two rows.
  • Show the intermediate value NOT A in multi-gate truth tables.
  • Use brackets to show what the NOT operation applies to.
  • Distinguish NOT (A AND B) from (NOT A) AND B.
  • Preserve double NOT gates if they appear in the given expression.
Common Mistakes
  • Giving NOT two inputs.
  • Leaving the input unchanged.
  • Applying NOT to the whole final expression when it applies to one variable.
  • Forgetting the output bubble in the symbol.
  • Removing a NOT gate as a simplification when the question asks for the given circuit.
Knowledge Check

1. What does NOT do to 0?

Answer: It changes 0 to 1.

2. What does NOT do to 1?

Answer: It changes 1 to 0.

3. How many rows are in a NOT truth table?

Answer: Two.

4. Is NOT (A AND B) the same structure as (NOT A) AND B?

Answer: No.

5. What symbol feature shows inversion?

Answer: A small circle or bubble.
PreviousNext