Number System Reference
Reference binary, octal, decimal, and hexadecimal number systems with clear examples and instant conversion lookup. Compare base rules, digit sets, and practical representations used in programming, networking, and systems work. Runs fully in your browser with no signup required.
Reference binary, octal, decimal, and hexadecimal systems with digit rules, practical examples, and instant cross-base conversion. Everything runs locally in your browser with no signup required.
| Decimal | Binary | Octal | Hexadecimal |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 2 | 10 | 2 | 2 |
| 7 | 111 | 7 | 7 |
| 8 | 1000 | 10 | 8 |
| 10 | 1010 | 12 | A |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
| 31 | 11111 | 37 | 1F |
| 64 | 1000000 | 100 | 40 |
| 255 | 11111111 | 377 | FF |
| 1024 | 10000000000 | 2000 | 400 |
Why Use Our Number System Reference?
Fast, accurate, and practical base-system reference for developers and learners
Instant Number System Lookup
View binary, octal, decimal, and hexadecimal formats instantly from one input. The number system reference updates in real time so you can cross-check representations without switching tools.
Accurate Base Conversion Logic
Conversions are performed using base-specific parsing and arbitrary-precision integer math, which keeps number system reference results consistent even for large values.
Built-In Example Table
Use the quick table of common values to understand how place-value boundaries work when numbers cross powers of two, eight, or sixteen.
Private and Browser-Based
This number system reference runs locally in your browser. No input is uploaded, no signup is required, and the tool is 100% free to use.
Common Use Cases for Number System Reference
Where binary, octal, decimal, and hexadecimal lookup is most useful
Programming and Debugging
Check hexadecimal memory values, binary bit masks, and decimal outputs quickly while debugging low-level code or reading logs.
Computer Science Learning
Students can compare the same value across base 2, 8, 10, and 16 to build intuition around radix systems and positional notation.
Networking and Security Workflows
Reference hexadecimal and binary representations while working with packet headers, flags, masks, and protocol values.
Embedded and Firmware Development
Use the number system reference to verify register values and configuration constants where hex and binary notation is standard.
Interview and Exam Preparation
Practice quick base conversion examples and review common conversion boundaries such as 8, 16, 255, and 1024.
Documentation and Technical Writing
Validate base-specific examples before publishing API docs, tutorials, or internal guides that include numeric literals.
Understanding Number Systems
A practical guide to binary, octal, decimal, and hexadecimal bases
What is a Number System?
A number system defines how numeric values are represented using a fixed set of symbols and a base (radix). The base determines how many unique digits are available before carrying into the next place. Decimal uses base 10, binary uses base 2, octal uses base 8, and hexadecimal uses base 16.
How Place Value Works
Each digit position represents a power of the base. In decimal, the value 345 means $3 \times 10^2 + 4 \times 10^1 + 5 \times 10^0$. In binary, 1011 means $1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 11$ in decimal. The same principle applies to every base.
Why Hexadecimal and Octal Are Useful
- Hexadecimal: Compactly represents binary values, with one hex digit mapping to exactly 4 binary bits.
- Octal: Maps cleanly to binary in groups of 3 bits, used in Unix permissions and some legacy systems.
- Decimal: Human-friendly for everyday arithmetic and reporting.
- Binary: Native representation for digital circuits and machine data.
How to Convert Between Bases
- Convert the source value to decimal by summing digit × base power.
- Convert decimal to target base using repeated division by the target radix.
- For binary↔hex and binary↔octal, use bit grouping (4 bits per hex, 3 per octal).
Frequently Asked Questions About Number System Reference
Common questions about base conversion and number representations
A number system reference is a guide that helps you understand and compare different bases such as binary, octal, decimal, and hexadecimal. It typically includes conversion examples, digit rules, and practical usage context for each system.
Base 2 uses digits 0-1, base 8 uses 0-7, base 10 uses 0-9, and base 16 uses 0-9 plus A-F. The base determines the place-value powers used to represent numbers and how many unique symbols each digit can take.
Hex is compact and maps directly to binary in 4-bit groups, which makes it ideal for representing bytes, memory addresses, bit masks, and color values like #FF5733. It is easier to read than long binary strings.
Yes. The conversion logic uses integer-safe parsing and big integer handling for high practical accuracy with large whole-number values across binary, octal, decimal, and hexadecimal systems.
Yes. The tool supports signed values with a leading minus sign. It converts the magnitude correctly and preserves sign across all output bases.
No. Everything runs locally in your browser and no values are uploaded to a server. Your conversion input remains private on your device.
Yes. The number system reference is 100% free with no signup, no account, and no usage limits. You can use it as often as you need.