Binary Converter
Convert binary to decimal, octal, and hexadecimal. Essential for computer science and programming.
Result
- Decimal (Base 10)
- -
- Octal (Base 8)
- -
- Hexadecimal (Base 16)
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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)
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.
Binary (base-2) uses only 0 and 1. It's the fundamental number system used by computers. Each digit represents a power of 2.
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.
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.
8-bit binary can represent values from 0 to 255. The maximum is 11111111 = 255 in decimal. This is one byte.
Computers use binary because electronic circuits can easily represent two states (on/off, high/low voltage). Binary is the foundation of all digital computing.
Yes, binary can be converted to decimal (base-10), octal (base-8), and hexadecimal (base-16). The calculator shows all conversions simultaneously.