The NOT Gate: Truth Table and Symbol

The NOT gate is the simplest logic gate. It takes a single input and produces the opposite (inverted) output. The NOT gate is also called an inverter. This is covered in OCR J277 Section 2.5.

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How the NOT Gate Works

The NOT gate performs negation. If the input is 1, the output is 0. If the input is 0, the output is 1. It simply flips the value.

In Boolean algebra, the NOT operation on input A is written as:

• NOT A
• A (with a bar over it, written as Ā)
• !A (in some programming languages)

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NOT Gate Truth Table

A	NOT A
0	1
1	0

This is the simplest truth table — just two rows because there is only one input. With one input there are 2^1 = 2 possible input values.

OCR Exam Tip: The NOT gate is the only standard logic gate with a single input. All other gates (AND, OR, XOR, NAND, NOR) take two inputs. If an exam question asks for a gate with one input, it is always NOT.

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NOT Gate Circuit Symbol

The standard NOT gate symbol used in OCR exams consists of:

1. A triangle pointing to the right
2. A small circle (called a "bubble") at the output

The triangle represents the gate body, and the bubble indicates inversion. You should be able to both recognise and draw this symbol in the exam.

flowchart LR
    A((A)) --> NOT["NOT gate"]
    NOT -->|NOT A| Q((Q))

The small circle at the tip of the triangle is the key feature that distinguishes the NOT gate from a simple buffer.

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NOT in Programming

In Python:

# Using the not keyword
logged_in = False
if not logged_in:
    print("Please log in")

In OCR pseudocode:

loggedIn = false
if NOT loggedIn then
    print("Please log in")
endif

The not operator inverts the Boolean value. Since logged_in is False, not logged_in evaluates to True, so the message is printed.

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Real-World Applications of NOT

The NOT gate has many practical uses in computing:

Application	How NOT is used
Toggle switches	Pressing a button inverts the current state (on becomes off, off becomes on)
Error detection	A NOT gate can invert a signal to check for the opposite condition
Building other gates	NOT is combined with AND and OR to create NAND and NOR gates
Bitwise NOT	Flipping all bits in a binary number (e.g., NOT 0110 = 1001)

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Bitwise NOT Operation

When NOT is applied to a whole binary number, it inverts every bit:

Input	NOT Output
0 0 0 0	1 1 1 1
1 0 1 0	0 1 0 1
1 1 0 0	0 0 1 1
0 1 1 1	1 0 0 0

This is sometimes called the one's complement of a binary number.

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Common Exam Mistakes

1. Forgetting the bubble — when drawing the NOT gate symbol, always include the small circle at the output. Without it, the symbol represents a buffer (which does not change the input).

2. Confusing NOT with subtraction — NOT does not subtract from a value. It inverts the Boolean state.

3. Incorrect truth table entries — some students accidentally write the same value for input and output. Remember: the output is always the opposite of the input.

OCR Exam Tip: If you are asked to "state the output" of a NOT gate for a given input, you can answer in one word or number. For example, "If A = 1, then NOT A = 0."

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Practice

Complete the following:

A	NOT A
1	?
0	?

Answers: NOT 1 = 0, NOT 0 = 1

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Summary

• The NOT gate inverts its single input: 0 becomes 1, and 1 becomes 0
• Its symbol is a triangle with a bubble at the output
• In Boolean algebra: NOT A or Ā
• The truth table has only 2 rows
• NOT is used in programming (not in Python, NOT in OCR pseudocode)
• NOT gates are fundamental building blocks for more complex circuits

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Worked Examples

Example 1: A single NOT inside a combined expression.

Evaluate Q = A AND (NOT B) when A = 1 and B = 0.

Step 1: NOT B = NOT 0 = 1. Step 2: Q = A AND (NOT B) = 1 AND 1 = 1.

Example 2: Double negation.

What does NOT (NOT A) evaluate to when A = 1?

Step 1: NOT A = NOT 1 = 0. Step 2: NOT (NOT A) = NOT 0 = 1.

So NOT (NOT A) = A. This identity is called the double negation law and is often used when simplifying Boolean expressions.

Example 3: NOT combined with OR.

Evaluate Q = (NOT A) OR B for every input combination.

A	B	NOT A	Q = (NOT A) OR B
0	0	1	1
0	1	1	1
1	0	0	0
1	1	0	1

Q is only 0 when A = 1 and B = 0. Every other input combination gives Q = 1.

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Full Truth Tables with NOT in Context

To understand NOT properly you need to see it working inside larger tables. Here is a 3-input expression using NOT on one variable:

Expression: Q = A AND B AND (NOT C)