Binary Base Converter

2

Conversion Results

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10
10
16
8
All-in-One Converter

Convert between any number base — binary, decimal, octal, hexadecimal, and ASCII text — all in one tool. With step-by-step calculations and digit grouping for readability.

5Number Systems
∞Precision
0msLatency

What is Binary Base Converter?

The Binary Base Converter is an all-in-one tool that lets you convert numbers between any combination of binary (base 2), decimal (base 10), octal (base 8), hexadecimal (base 16), and ASCII text — all in a single interface. Instead of switching between separate converters, this tool handles every base conversion you need.

This tool exists because developers, students, and engineers frequently need to work across multiple number systems simultaneously. Whether you're translating memory addresses from hex to binary, converting file permissions from octal to decimal, or decoding ASCII text, this converter provides instant cross-base translation with step-by-step explanations.

Understanding how different number bases relate to each other is foundational in computer science, digital electronics, and systems programming — and this tool makes those conversions effortless.

Interactive Demo

Binary Base Converter Formula

Enter any decimal number below to see it displayed simultaneously in all four major number systems.

Base Explorer
Binary (Base 2)
11111111
Decimal (Base 10)
255
Octal (Base 8)
377
Hexadecimal (Base 16)
FF
Concept Guide

Why Different Bases Exist

2
Binary
The language of hardware. Transistors have two states — on and off — making base 2 the fundamental language of all digital circuits, CPUs, and memory.
8
Octal
Groups 3 binary bits. Historically used with 12/24/36-bit computers. Still used today in Unix chmod file permissions (e.g., 755).
16
Hexadecimal
Groups 4 binary bits (one nibble). The standard in modern computing for memory addresses, color codes (#FF5733), MAC addresses, and debugging.
Quick Reference

Powers of 2 Table

Essential values every programmer should know — from single bits to 64-bit boundaries.

PowerDecimalBinaryHexCommon Name
2⁰111—
2⁴161000010Nibble max + 1
2⁷1281000000080ASCII range
2⁸256100000000100Byte max + 1
2¹⁰1,024100000000004001 KiB
2¹⁶65,536—10000Short max + 1
2²⁰1,048,576—1000001 MiB
2³⁰1,073,741,824—400000001 GiB
2³²4,294,967,296—100000000Int max + 1
More

Other Number System Conversions

Related numeral systems converters for number conversion between binary, decimal, hexadecimal, octal, and ASCII text.

01→10 Binary to Decimal Converter 01.1→10 Binary Fraction to Decimal ±01→10 Signed Binary to Decimal 01→FF Binary to Hexadecimal 01→07 Binary to Octal 01+01 Binary Calculator 01+01 Binary Addition 01−01 Binary Subtraction → 1,2,3 Step-by-Step Solver 0…255 Binary Table Generator 01→A Binary to Text A→01 Text to Binary ±1.M×2ᴱ Floating Point Converter 8b→256 Bit Size Converter & | ^ ~ Bitwise Operations 01→? Binary Decoder
FAQ

Frequently Asked Questions

What is a number base (radix)?
A number base (or radix) is the number of unique digits used to represent numbers in a positional numeral system. Binary uses base 2 (digits 0-1), octal uses base 8 (digits 0-7), decimal uses base 10 (digits 0-9), and hexadecimal uses base 16 (digits 0-F). Each position in a number represents a power of the base.
How do you convert between different number bases?
The general method: first convert the source number to decimal (base 10) by multiplying each digit by its positional power of the source base, then convert the decimal value to the target base by repeatedly dividing by the target base and recording remainders. Some pairs (like binary↔hex) have shortcut grouping methods.
What are the most common number bases in computing?
Binary (base 2) is used internally by all computers. Decimal (base 10) is human-readable output. Hexadecimal (base 16) is used for memory addresses, color codes, and debugging. Octal (base 8) is used in Unix permissions. ASCII maps numbers to text characters.
Why do computers use binary instead of decimal?
Computers use binary because electronic circuits have two stable states: on (1) and off (0). Distinguishing between 2 voltage levels is far simpler and more reliable than distinguishing between 10. Binary arithmetic is also simpler to implement in hardware, requiring fewer transistors.
Can you convert directly between hex and octal?
The easiest method is to convert via binary as an intermediate step. Convert hex to binary (expand each hex digit to 4 bits), then re-group the binary bits into 3-bit groups for octal. Direct hex-to-octal conversion without an intermediate step is possible but more complex.
What is the relationship between binary, octal, and hex?
All three are power-of-2 bases: binary is 2¹, octal is 2³, and hex is 2⁴. This means octal groups 3 binary bits and hex groups 4 binary bits. This power-of-2 relationship makes conversions between them simple grouping operations rather than complex arithmetic.
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