Generating Binary Numbers Using Queues in Python

Hey folks! 👋 Today I dove into an interesting problem involving queues and binary numbers — and I want to share what I learned in a simple way.

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What Are Binary Numbers?

Binary numbers are just numbers made up of only 0s and 1s — the base language of computers. For example:

• Decimal 1 = Binary 1

• Decimal 2 = Binary 10

• Decimal 3 = Binary 11

• Decimal 4 = Binary 100

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The Challenge

How do you generate the first n binary numbers in order, without converting each decimal number one by one?

The answer: use a queue and build them step-by-step like a binary tree!

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How Does It Work?

We start with '1' in a queue. Each time we:

1. Pop the front binary number from the queue.

2. Add it to our result list.

3. Append two new numbers to the queue:

   • The current number + '0'

   • The current number + '1'

This way, every number generates two “children” by adding a 0 or 1, like this binary tree:

        1
      /   \
    10     11
   /  \   /  \
 100 101 110 111

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Here’s the Code!

from collections import deque

def generate_binary_numbers(n):
    queue = deque(['1'])
    result = []

    for _ in range(n):
        front = queue.popleft()
        result.append(front)

        queue.append(front + '0')
        queue.append(front + '1')

    return result

n = int(input("Enter the number of binary numbers to generate: "))
print(generate_binary_numbers(n))

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Why Use This Approach?

• No need to convert from decimal — we directly build the binary numbers as strings.

• It’s a clean, logical way to generate sequences using queues and trees.

• Helps you understand breadth-first traversal and the power of queues.

• Great for coding interviews and algorithm practice!

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Real-World Applications

• Generating all bit sequences of length n for network protocols.

• Building binary decision trees.

• Encoding problems and compression algorithms.

• Any situation where you need to systematically generate combinations.

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Final Thoughts

Queues aren’t just about waiting in line — they’re a powerful data structure to generate sequences like binary numbers efficiently and clearly. If you’re new to queues, this is a great exercise to deepen your understanding.