🔌 Logic Gates Overview

🔌 Logic Gates Overview#

Logic gates are the fundamental building blocks of digital circuits. They perform basic logical operations on one or more binary inputs to produce a single binary output.

Each gate follows a truth table that defines its behavior based on input combinations.

🧠 Types of Logic Gates#

1. AND Gate#

  • Symbol: ⋅

  • Operation: Output is 1 only if both inputs are 1.

  • Truth Table:

    A

    B

    Output

    0

    0

    0

    0

    1

    0

    1

    0

    0

    1

    1

    1

2. OR Gate#

  • Symbol: +

  • Operation: Output is 1 if at least one input is 1.

  • Truth Table:

    A

    B

    Output

    0

    0

    0

    0

    1

    1

    1

    0

    1

    1

    1

    1

3. NOT Gate#

  • Symbol: ¬ or !

  • Operation: Inverts the input (0 becomes 1, 1 becomes 0).

  • Truth Table:

    A

    Output

    0

    1

    1

    0

4. NAND Gate#

  • Operation: Opposite of AND. Output is 0 only if both inputs are 1.

  • Truth Table:

    A

    B

    Output

    0

    0

    1

    0

    1

    1

    1

    0

    1

    1

    1

    0

5. NOR Gate#

  • Operation: Opposite of OR. Output is 1 only if both inputs are 0.

  • Truth Table:

    A

    B

    Output

    0

    0

    1

    0

    1

    0

    1

    0

    0

    1

    1

    0

6. XOR Gate (Exclusive OR)#

  • Operation: Output is 1 if inputs are different.

  • Truth Table:

    A

    B

    Output

    0

    0

    0

    0

    1

    1

    1

    0

    1

    1

    1

    0

7. XNOR Gate (Exclusive NOR)#

  • Operation: Output is 1 if inputs are the same.

  • Truth Table:

    A

    B

    Output

    0

    0

    1

    0

    1

    0

    1

    0

    0

    1

    1

    1

📘 Summary Table#

Gate

Symbol

Operation Description

Output is 1 When…

AND

⋅

Both inputs are 1

A = 1 and B = 1

OR

+

At least one input is 1

A = 1 or B = 1

NOT

¬

Inverts the input

A = 0

NAND

¬(A⋅B)

Opposite of AND

Not both A and B are 1

NOR

¬(A+B)

Opposite of OR

Both A and B are 0

XOR

⊕

Inputs are different

A ≠ B

XNOR

¬(A⊕B)

Inputs are the same

A = B

Logic gates are used to build combinational and sequential circuits, forming the backbone of processors, memory units, and digital systems.

import ipywidgets as widgets
from IPython.display import display, Markdown, clear_output

# 🔘 Input Widgets
input_a = widgets.ToggleButton(value=False, description='Input A', button_style='info')
input_b = widgets.ToggleButton(value=False, description='Input B', button_style='info')

gate_selector = widgets.Dropdown(
    options=['AND', 'OR', 'NOT', 'NAND', 'NOR', 'XOR', 'XNOR'],
    value='AND',
    description='🔀 Select Gate:',
    style={'description_width': 'initial'},
    layout=widgets.Layout(width='300px')
)

output_area = widgets.Output()

### 🧠 Logic Gate Functions
gate_functions = {
    'AND': lambda a, b: a and b,
    'OR': lambda a, b: a or b,
    'NOT': lambda a, _: not a,
    'NAND': lambda a, b: not (a and b),
    'NOR': lambda a, b: not (a or b),
    'XOR': lambda a, b: a != b,
    'XNOR': lambda a, b: a == b
}

### 📊 Truth Table Generator
def generate_truth_table(gate):
    rows = []
    for a in [0, 1]:
        for b in [0, 1]:
            result = gate_functions[gate](bool(a), bool(b)) if gate != 'NOT' else gate_functions[gate](bool(a), None)
            rows.append(f"| {a} | {b if gate != 'NOT' else '-'} | {int(result)} |")
    header = "| A | B | Output |\n|---|---|--------|"
    return header + "\n" + "\n".join(rows)

### 🔄 Update Display
def update_output(change=None):
    output_area.clear_output()
    a = input_a.value
    b = input_b.value
    gate = gate_selector.value
    result = gate_functions[gate](a, b) if gate != 'NOT' else gate_functions[gate](a, None)

    with output_area:
        display(Markdown(f"### ⚙️ Logic Gate: `{gate}`"))
        display(Markdown(f"**Input A:** `{int(a)}`  \n**Input B:** `{int(b) if gate != 'NOT' else 'N/A'}`"))
        display(Markdown(f"**Output:** `{int(result)}`"))
        display(Markdown("### 📊 Truth Table"))
        display(Markdown(generate_truth_table(gate)))

### 🔁 Observe Changes
input_a.observe(update_output, names='value')
input_b.observe(update_output, names='value')
gate_selector.observe(update_output, names='value')

### 🚀 Display Interface
display(widgets.HBox([input_a, input_b]))
display(gate_selector)
display(output_area)
update_output()
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