Binary to Decimal: Visual Guide
Level 3: Decoding the language of computers and digital logic.
🔢 What is Binary?
Binary is a base-2 numbering system that uses only two symbols: 0 and 1. In electronics, these represent “OFF” and “ON” states. While humans use decimal (base-10), computers use binary to process everything from simple math to complex graphics.
📐 The Method: Positional Notation
To convert binary to decimal, you multiply each bit by 2 raised to the power of its position (starting from 0 on the right).
Example: 1011
(1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰)
8 + 0 + 2 + 1 = 11
🔍 The Power of 2 Table
Memorizing these values makes conversion instant:
- 2⁷ = 128
- 2⁶ = 64
- 2⁵ = 32
- 2⁴ = 16
- 2³ = 8
- 2² = 4
- 2¹ = 2
- 2⁰ = 1
🚀 Real-World Example: IP Addresses
Every time you connect to the internet, your computer uses an IP address. While we see them as numbers like 192.168.1.1, the network hardware sees four sets of 8-bit binary numbers (octets). Understanding binary is the key to understanding how the entire internet communicates!
The Light Switch Analogy
Think of binary like a row of light switches. Each switch has a value (1, 2, 4, 8, etc.). If the switch is “1” (ON), you add its value to your total. If it’s “0” (OFF), you ignore it. The decimal number is simply the sum of all the “ON” switches!