The NOT Gate

The NOT gate is the simplest of all logic gates. It has a single input and a single output, and its job is to invert (reverse) whatever value it receives. If the input is 1, the output is 0. If the input is 0, the output is 1.

---

How the NOT Gate Works

The NOT gate performs the Boolean operation of negation (also called inversion or complementation). It takes one input and produces the opposite value as its output.

• If the input is 1 (TRUE), the output is 0 (FALSE).
• If the input is 0 (FALSE), the output is 1 (TRUE).

Think of the NOT gate as a simple "flip" — it always gives you the opposite of what you put in.

---

Truth Table for NOT

The truth table for a NOT gate is the simplest of all logic gates because there is only one input:

Input (A)	Output (¬A)
0	1
1	0

The block view of the gate matches this truth table — a single input flowing through NOT produces the inverted output:

graph LR
    A((A)) --> NOT["NOT"]
    NOT --> Q((Q = NOT A))

The output column is labelled ¬A (read as "NOT A"). Some textbooks and exam papers use the notation A̅ (A with a bar over the top) instead of ¬A — both mean exactly the same thing.

---

Logic Gate Symbol

The standard symbol for a NOT gate (used in both British and international standards) looks like a triangle pointing to the right with a small circle (called a bubble) at the output:

        +-----\
  A ----|      >o---- Output (¬A)
        +-----/

Key features of the NOT gate symbol:

• The triangle represents the gate body.
• The small circle (bubble) at the tip indicates inversion — this is what makes it a NOT gate rather than just a buffer.
• The single line on the left is the input (A).
• The line on the right (after the bubble) is the output (¬A).

---

Boolean Expression

The Boolean expression for a NOT gate is written as:

¬A or NOT A or A̅

All three notations are acceptable in GCSE exams, but ¬A is the most commonly used in AQA and OCR specifications.

If you see a Boolean expression like ¬B, it simply means "the opposite of B":

• If B = 1, then ¬B = 0
• If B = 0, then ¬B = 1

---

Real-World Analogy

A good way to think about a NOT gate is as a light switch inverter:

• When the switch is ON (1), the light is OFF (0).
• When the switch is OFF (0), the light is ON (1).

This might seem backwards, but there are real-world examples of this — some security systems have a "normally closed" switch where the alarm is active (output = 1) when the switch is NOT pressed (input = 0), and the alarm deactivates (output = 0) when the switch IS pressed (input = 1).

---

NOT in Programming

In programming languages, the NOT operation is used to reverse a Boolean condition:

Python:

logged_in = False
if not logged_in:
    print("Please log in.")

JavaScript:

let loggedIn = false;
if (!loggedIn) {
    console.log("Please log in.");
}

In Python, the keyword is not. In many other languages (JavaScript, Java, C#), the symbol ! is used.

---

Double NOT (Double Negation)

Applying NOT twice returns you to the original value:

¬(¬A) = A

A	¬A	¬(¬A)
0	1	0
1	0	1

This is called the double negation rule or the involution law. It is a useful simplification rule in Boolean algebra — if you see two NOT operations applied to the same variable, they cancel each other out.

---

The NOT Gate in Circuits

In electronic circuits, a NOT gate is typically built from one or two transistors. When the input voltage is high (representing 1), the transistor configuration causes the output voltage to be low (representing 0), and vice versa.

NOT gates are also called inverters in electronics. They are among the most commonly used components in digital circuit design.

Common uses of NOT gates:

• Signal inversion — converting an active-high signal to active-low (or vice versa).
• Building other gates — NOT gates are combined with AND and OR gates to create NAND, NOR and other complex gates.
• Toggle circuits — used in flip-flops and other memory circuits.

---

Exam-Style Questions to Consider

1. Draw the truth table for a NOT gate. (2 marks)
2. Write the Boolean expression for a NOT gate with input P. (1 mark)
3. Draw the logic gate symbol for a NOT gate. (1 mark)
4. Explain what happens when a NOT operation is applied twice to the same input. (2 marks)

Exam Tip: The NOT gate is the only gate with a single input. If an exam question asks about a gate with one input, it must be a NOT gate. Remember the bubble on the symbol — this is the key identifier for inversion and also appears on NAND and NOR gate symbols.

---

Summary

• The NOT gate has one input and one output.
• It inverts the input: 0 becomes 1, and 1 becomes 0.
• The Boolean expression is ¬A (or A̅ or NOT A).
• The symbol is a triangle with a bubble at the output.
• Double negation cancels out: ¬(¬A) = A.
• NOT gates are also called inverters and are used as building blocks for more complex gates.

---

Worked Examples Using NOT

Worked Example 1: NOT in a Two-Input Expression

Consider the expression ¬A ∧ B — read as "NOT A AND B". This is a classic combination tested at GCSE.