Binary numbers are a way of writing numbers using only two digits: 0 and 1, instead of the ten digits 0–9 that we use in normal decimal notation.

Quick Scoop

In the binary (base‑2) system, each position in a number represents a power of 2, just like each position in decimal represents a power of 10.

From right to left, the places are 20,21,22,23,2^0,2^1,2^2,2^3,20,21,22,23, and so on.

Example:

  • Binary number 1001₂ means
    • 1×23=81\times 2^3=81×23=8
    • 0×22=00\times 2^2=00×22=0
    • 0×21=00\times 2^1=00×21=0
    • 1×20=11\times 2^0=11×20=1
      → total = 9 in decimal.

Another example often used in tutorials: 11001₂ = 25 in decimal, because
1×16+1×8+0×4+0×2+1×1=25.1\times 16+1\times 8+0\times 4+0\times 2+1\times 1=25.1×16+1×8+0×4+0×2+1×1=25.

Why binary matters (today’s context)

  • It is the fundamental language of computers and digital electronics.
  • Every piece of data—text, images, audio, video, apps—is ultimately stored and processed as long sequences of 0s and 1s.
  • Modern processors, microcontrollers, and digital circuits are built from components that have two stable states, which naturally map to 0 and 1.

Tiny “story” to picture it

Imagine a huge city where every house can only have the lights either fully off (0) or fully on (1).
If you stand on a hill and look at a row of these houses at night, the pattern of lights—off/on/on/off…—forms a code.
Each light in a specific position is worth a certain “weight” (1, 2, 4, 8, 16, …), and when you sum the weights of the houses that are lit, you get a normal decimal number. That’s essentially what a computer does with binary.

Common quick facts

  • Binary = base‑2 number system (only digits 0 and 1).
  • Each digit is called a bit (short for “binary digit”).
  • 0–10 in binary look like:
    • 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010.
  • Binary is one of several standard number systems; others include decimal (base 10), octal (base 8), and hexadecimal (base 16).

A quick HTML table of small numbers

html

<table>
  <thead>
    <tr>
      <th>Decimal</th>
      <th>Binary</th>
    </tr>
  </thead>
  <tbody>
    <tr><td>0</td><td>0</td></tr>
    <tr><td>1</td><td>1</td></tr>
    <tr><td>2</td><td>10</td></tr>
    <tr><td>3</td><td>11</td></tr>
    <tr><td>4</td><td>100</td></tr>
    <tr><td>5</td><td>101</td></tr>
    <tr><td>6</td><td>110</td></tr>
    <tr><td>7</td><td>111</td></tr>
    <tr><td>8</td><td>1000</td></tr>
    <tr><td>9</td><td>1001</td></tr>
    <tr><td>10</td><td>1010</td></tr>
  </tbody>
</table>

Information gathered from public forums or data available on the internet and portrayed here.