What is Binary?

Introduction

Binary is a base-2 numeral system that uses only two digits: 0 and 1. It serves as the foundation of digital technology and computer systems. Every piece of data processed by a computer—whether text, images, or videos—is represented in binary. Understanding binary is essential for grasping how computers store, process, and transmit information.

Table of Contents

What is Binary?

Binary is a numerical system that operates on base-2, unlike the decimal system, which is base-10. It uses only two symbols: 0 and 1, which are known as bits (short for binary digits). These bits represent the on and off states in electronic circuits, making binary a natural fit for computers and digital systems.

How Binary Works

Each digit in a binary number represents a power of 2, starting from the rightmost digit (similar to how each digit in a decimal number represents a power of 10).

For example, the binary number 1011 can be expanded as:
1 × 2³ + 0 × 2² + 1 × 2¹ + 1 × 2⁰ = 8 + 0 + 2 + 1 = 11 (decimal)

Binary vs. Decimal System

Feature Binary (Base-2) Decimal (Base-10)
Symbols Used 0, 1 0, 1, 2, …, 9
Representation Powers of 2 Powers of 10
Example 1011 = 11 11 = 11

Binary is simpler for machines to process but less intuitive for humans compared to the decimal system.

Applications of Binary in Computing

Data Representation
Binary encodes data such as text, images, and videos into sequences of 0s and 1s. For instance:

  • ASCII code represents characters like ‘A’ as binary numbers (e.g., 01000001).

Logic Gates and Circuits
Computers use binary to represent logical operations in hardware, using gates like AND, OR, and NOT.

File Formats
Every file on a computer, from documents to executables, is stored as a sequence of binary data.

Converting Binary to Decimal and Vice Versa

Binary to Decimal
Expand each binary digit using powers of 2. For example:

Binary: 1101
(1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰) = 8 + 4 + 0 + 1 = 13 (decimal)

Decimal to Binary
Divide the decimal number by 2, recording the remainder, until the quotient is 0. Then reverse the remainders.

Example: Convert 13 to binary.

  1. 13 ÷ 2 = 6 remainder 1
  2. 6 ÷ 2 = 3 remainder 0
  3. 3 ÷ 2 = 1 remainder 1
  4. 1 ÷ 2 = 0 remainder 1
    Binary: 1101

Conclusion

Binary is the fundamental language of computers, shaping how digital systems function and communicate. While it might seem abstract, binary’s simplicity allows machines to perform complex operations with incredible speed and accuracy. By understanding binary, we can better appreciate the inner workings of the technology that powers our modern world.