Free Number System Converter: Binary, Octal, Decimal and Hex — All at Once
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Switching between number systems is one of the most frequent — and most frustrating — tasks in computer science, electronics, and programming. Whether you are converting a decimal value to binary for a coding exercise, translating a hex color code to RGB, checking Unix file permissions in octal, or debugging memory addresses, stopping to do it manually wastes time. The Number System Converter by ExcelGuru does it all instantly, in one place, for free.
Enter any number in Binary, Octal, Decimal, Hexadecimal, Base 32 or Base 36 — see every other base immediately, plus a 32-bit visualiser, Two’s Complement, and IEEE 754 float representation.
What Is a Number System Converter?
A number system converter — also called a base converter or radix converter — is a tool that translates a number expressed in one base into its equivalent in other bases. The most commonly used bases in computing are:
- Binary (Base 2) — uses only 0 and 1. The fundamental language of all digital hardware.
- Octal (Base 8) — uses digits 0 to 7. Still widely used for Unix/Linux file permissions (chmod 755).
- Decimal (Base 10) — the everyday human number system, digits 0 to 9.
- Hexadecimal (Base 16) — uses digits 0–9 and letters A–F. Used for memory addresses, color codes, and compact binary representation.
Our converter also supports Base 32 and Base 36 — useful in URL shorteners, identifier generation, and encoding systems where a compact alphanumeric representation is needed.
Quick Conversion Reference Table
Decimal | Binary | Octal | Hex |
255 | 11111111 | 377 | FF |
16 | 10000 | 20 | 10 |
10 | 1010 | 12 | A |
128 | 10000000 | 200 | 80 |
65535 | 1111111111111111 | 177777 | FFFF |
0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 |
What the ExcelGuru Number System Converter Includes
All 6 bases — live, simultaneous
Type any value into the input field, select its base from the dropdown, and all six base representations update instantly. Every result has a Copy button so you can grab any value with one click.
32-bit Binary Visualizer
The 32-bit visualizer displays all 32 individual bit cells — green for 1, grey for 0 — grouped into 4 bytes of 8 bits each. Below it, you see set bit count, clear bit count, MSB (most significant bit), LSB (least significant bit), and all four individual byte values in hex. This is invaluable when working with bitmasks, bitwise operations, or hardware registers.
Two’s Complement
Two’s complement is the standard way computers represent signed (positive and negative) integers. The converter shows the unsigned 32-bit value (uint32), the signed 32-bit value (int32), the bitwise NOT (~n), the two’s complement itself, and the signed hex value. For example, -1 in 32-bit two’s complement is 0xFFFFFFFF.
IEEE 754 Single Precision (32-bit Float)
The IEEE 754 section shows how your decimal value is stored as a 32-bit floating point number, colour-coded by component: the sign bit (red), the 8 exponent bits (amber), and the 23 mantissa bits (blue). It also shows the biased exponent, the actual exponent value, the full 32-bit hex representation, and handles special values like NaN, positive infinity, and negative infinity.
Conversion History
The last 15 conversions are stored in a history log. Click any entry to reload it instantly — useful when you are working through a series of values and need to jump back.
Who Uses a Number System Converter?
Number system converters are used across a wide range of fields and contexts:
- Computer science students completing assignments in digital logic, computer architecture, and discrete mathematics
- Software developers working with memory addresses, bitwise operations, and low-level data structures
- Web designers converting hex color codes like #FF5733 to their RGB decimal equivalents
- Network engineers working with IP addresses, MAC addresses, and subnet masks in binary and hex
- System administrators setting Linux file permissions using octal (chmod 755 = rwxr-xr-x in binary)
- Embedded systems engineers programming microcontrollers and reading hardware register values in hex
How to Use the Number System Converter
- Type any number into the input field at the top of the tool
- Select the base of your input from the dropdown (Binary, Octal, Decimal, Hex, Base 32 or Base 36)
- All six base representations appear instantly in the results panel
- Click “Copy” on any result to copy it to your clipboard
- Expand the 32-bit visualizer to see the individual bit pattern
- Click any history entry to reload that conversion
The tool validates your input in real time — if you type a character that does not belong to the selected base (e.g. the digit 9 in binary), it shows an immediate error and tells you exactly what went wrong.
Real-World Conversion Examples
Converting 255 to all bases — 255 is the maximum value of a single unsigned byte (8 bits). In binary it is 11111111, in hex it is FF, in octal it is 377. This is why web colors go from #000000 to #FFFFFF.
Unix permissions — 755 in octal — When you run chmod 755 on a Linux file, 7 in octal is 111 in binary (read+write+execute for owner), and 5 in octal is 101 (read+execute for group and others). The converter shows you this instantly.
Hex color to decimal — #22C55E — The ExcelGuru brand green in decimal is Red 34, Green 197, Blue 94. Enter 22 in hex to get 34 decimal for red, 1F in hex to get 31 for blue, and so on.
Frequently Asked Questions
Does the converter work with negative numbers?
Yes. The Two’s Complement panel shows how negative integers are represented in 32-bit signed binary. Enter a negative decimal value and the tool shows the int32 signed representation, the bitwise NOT, and the two’s complement in hex.
What is the maximum number supported?
The tool works accurately with integers up to JavaScript’s safe integer limit (2^53 – 1 = 9,007,199,254,740,991). For very large numbers the IEEE 754 panel may show rounding due to 32-bit float precision limits.
Does it work offline?
Yes. Once loaded in your browser, the Number System Converter runs entirely offline. All conversion logic is built into the single HTML file — nothing is sent to any server. You can also save the file to your device for permanent offline access.