How do I read binary?

Each digit represents a power of 2. From right to left: 1, 2, 4, 8, 16, 32... Example: 1011 = 8+0+2+1 = 11 in decimal.

How do I convert binary to decimal?

Multiply each digit by its corresponding power of 2 (starting from right, power 0), then sum the results. Example: 1010 = (1×8) + (0×4) + (1×2) + (0×1) = 10.

What is the maximum value in 8-bit binary?

8-bit binary can represent values from 0 to 255. The maximum is 11111111 = 255 in decimal. This is one byte.

Why do computers use binary?

Computers use binary because electronic circuits can easily represent two states (on/off, high/low voltage). Binary is the foundation of all digital computing.

Can I convert binary to other number systems?

Yes, binary can be converted to decimal (base-10), octal (base-8), and hexadecimal (base-16). The calculator shows all conversions simultaneously.

Binary Converter

Convert binary to decimal, octal, and hexadecimal. Essential for computer science and programming.

Converter

Binary (Base 2)

Result

Decimal (Base 10): -
Octal (Base 8): -
Hexadecimal (Base 16): -

Conversion Guide

Conversion

B

Binary to Decimal

Sum of (digit × 2^position)

Multiply each digit by its power of 2, sum results

H

Binary to Hex

Group 4 bits → Hex digit

Group binary digits into 4-bit chunks, convert to hex

Step-by-Step Scenario

Example Scenario

Binary

1010

1

Assign Powers

From right: 2⁰, 2¹, 2², 2³ = 1, 2, 4, 8

Assign power of 2 to each position

2

Calculate

(1×8) + (0×4) + (1×2) + (0×1)

10 (decimal)

Additional Examples

8-bit Binary

Binary: 11111111

Decimal

255

Hex

FF

Simple Binary

Binary: 1100

Decimal

12

Hex

C

Characteristics of Binary

Computer Foundation

Binary (base-2) is the fundamental number system used by computers. All digital data is represented in binary.

Multiple Conversions

Convert binary to decimal, octal, and hexadecimal simultaneously. Essential for programming and computer science.

Real-Time Conversion

Convert binary instantly as you type. Invalid binary digits are automatically filtered.

Two Digits Only

Binary uses only 0 and 1. Each digit represents a power of 2, making it the simplest number system.

Important Notes

Binary (base-2) uses only digits 0 and 1. Each position represents a power of 2, starting from the right (2⁰, 2¹, 2², ...).
To convert binary to decimal, multiply each digit by its corresponding power of 2 and sum the results.
Binary to hexadecimal: group binary digits into 4-bit chunks (from right), convert each chunk to hex (0-F).
Binary to octal: group binary digits into 3-bit chunks (from right), convert each chunk to octal (0-7).
8 bits = 1 byte. 8-bit binary can represent values from 0 to 255 (2⁰- 1).

Frequently Asked Questions

Find answers to common questions about binary conversion.