🔢 Number Systems Overview

A number system is a structured way to represent and manipulate numbers using a set of symbols and rules. Each system has a base that determines how many unique digits it uses.

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🌍 Types of Number Systems

Number System	Base	Digits Used	Example	Common Uses
Decimal	10	0–9	42	Everyday arithmetic, finance
Binary	2	0, 1	101010	Computers, digital circuits
Octal	8	0–7	52	Unix file permissions, legacy code
Hexadecimal	16	0–9, A–F	2A	Memory addressing, color codes

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🧠 Key Differences

• Base Value:
  Determines how many digits are used before rolling over to the next place value.

• Digit Set:
  Binary uses only 0 and 1, while hexadecimal includes letters A–F for values 10–15.

• Compactness:
  Binary numbers are longer; hexadecimal and octal offer more compact representations.

• Conversion:
  All systems can be converted to and from decimal. For example:

  • Binary 101010 → Decimal 42

  • Decimal 42 → Hexadecimal 2A

  • Decimal 42 → Octal 52

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📘 Summary Table

Feature	Decimal	Binary	Octal	Hexadecimal
Base	10	2	8	16
Digits Used	0–9	0, 1	0–7	0–9, A–F
Example	42	101010	52	2A
Compactness	Moderate	Least	More than binary	Most
Use Case	Daily life	Computers	Legacy systems	Programming

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Understanding these systems is essential for fields like computer science, engineering, and cybersecurity, where data representation and manipulation are foundational.

🔄 Interactive Number System Converter

This tool allows users to convert numbers between Decimal, Binary, Octal, and Hexadecimal systems using Python and ipywidgets.

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🧠 What It Does

• Accepts a number input and its base (e.g., Decimal, Binary).

• Converts it to a target base selected by the user.

• Displays the result and a brief interpretation.

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⚙️ How It Works

1. Input Handling:
   The user enters a number and selects its base (e.g., Decimal).

2. Conversion Logic:

   • The input is first converted to Decimal using int(num_str, base_from).

   • Then it’s converted to the target base using:

     • bin() for Binary

     • oct() for Octal

     • hex() for Hexadecimal

3. Output Display:
   The result is shown using Markdown formatting, along with a clear explanation of the conversion.

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✅ Example

Input:

• Number: 42

• From Base: Decimal

• To Base: Binary

Output:

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

# 🔢 Supported Bases
bases = {
    "Decimal": 10,
    "Binary": 2,
    "Octal": 8,
    "Hexadecimal": 16
}

# 📥 Input Widgets
input_number = widgets.Text(
    value='42',
    description='🔢 Input Number:',
    style={'description_width': 'initial'},
    layout=widgets.Layout(width='400px')
)

input_base = widgets.Dropdown(
    options=bases.keys(),
    value='Decimal',
    description='📥 From Base:',
    style={'description_width': 'initial'},
    layout=widgets.Layout(width='300px')
)

output_base = widgets.Dropdown(
    options=bases.keys(),
    value='Binary',
    description='📤 To Base:',
    style={'description_width': 'initial'},
    layout=widgets.Layout(width='300px')
)

output = widgets.Output()

# 🔄 Conversion Logic
def convert_number(change=None):
    output.clear_output()
    try:
        base_from = bases[input_base.value]
        base_to = bases[output_base.value]
        num_str = input_number.value.strip()

        # Convert input to decimal
        decimal_value = int(num_str, base_from)

        # Convert decimal to target base
        if base_to == 2:
            converted = bin(decimal_value)[2:]
        elif base_to == 8:
            converted = oct(decimal_value)[2:]
        elif base_to == 16:
            converted = hex(decimal_value)[2:]
        else:
            converted = str(decimal_value)

        with output:
            display(Markdown(f"### ✅ Result"))
            display(Markdown(f"**{input_base.value} {num_str} → {output_base.value} {converted}**"))
            display(Markdown(f"**📘 Interpretation:** Converted from base {base_from} to base {base_to} using Python's built-in conversion functions."))

    except ValueError:
        with output:
            display(Markdown("❌ **Invalid input for the selected base. Please check your number format.**"))

# 🔁 Observe Changes
input_number.observe(convert_number, names='value')
input_base.observe(convert_number, names='value')
output_base.observe(convert_number, names='value')

# 🚀 Display Widgets
display(widgets.HBox([input_base, output_base]))
display(input_number)
display(output)
convert_number()