Convert between decimal, binary, hex, and octal. Includes Unicode inspector, IP address converter, IEEE 754 float visualizer, bit-width selector, and signed/unsigned bitwise operations.
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Enter a number in any base to see all conversions
This free binary hex converter is an all-in-one number base converter that instantly translates between decimal, binary, hexadecimal, and octal, while also covering four related developer tasks in one place: a Unicode/ASCII code lookup with UTF-8 and UTF-16 byte encoding, an IPv4/IPv6 address to binary tool with subnet mask breakdown, an IEEE 754 floating-point visualizer for both 32-bit and 64-bit precision, and signed/unsigned bitwise operations (AND, OR, XOR, NOT, shifts) across 8, 16, 32, or 64-bit widths. Whether you need a quick decimal to binary converter for a homework problem, a hex to binary tool for debugging memory addresses, or an IEEE 754 visualizer to understand why 0.1 + 0.2 doesn't equal 0.3 exactly, this single tool replaces several separate developer utilities.
The Number Converter tab converts any value you type into decimal, binary, hexadecimal, or octal instantly, alongside a visual bit display and quick-preset buttons for common values like 255, 1024, and 65535. It also includes bitwise operators (AND, OR, XOR, NOT, left/right shift) with a signed/unsigned toggle, and a Unicode/ASCII lookup that shows a character's code point, UTF-8 bytes, and UTF-16 units. The IP Address tab breaks an IPv4 or IPv6 address into its per-octet or per-hextet decimal, hex, and binary form, and detects subnet mask patterns. The IEEE 754 Float tab visualizes the sign bit, exponent, and mantissa of any decimal number in both single (32-bit) and double (64-bit) precision.
This tool is built for software developers debugging bit-level flags or memory values, computer science students learning number systems and floating-point representation, network engineers calculating subnet masks and IP ranges, and anyone curious why 0.1 + 0.2 gives 0.30000000000000004 in nearly every programming language. It also serves students and hobbyists exploring Unicode encoding for non-English text and emoji.
Computers store everything in binary, but binary is unwieldy for humans to read, so hexadecimal (compact, 4 bits per digit) and decimal (familiar) serve as human-friendly shorthand. Understanding how these bases relate is foundational to reading memory dumps, color codes, IP addresses, and register values — and IEEE 754 float representation explains one of the most common sources of confusion in programming: why decimal fractions don't always add up exactly in floating-point arithmetic.
Software developers use hex to read memory addresses, debug bit flags, and work with color codes (#RRGGBB). Network engineers convert IP addresses to binary to calculate subnet masks and valid host ranges. Embedded systems programmers manipulate register values and bitwise flags directly. Text-processing applications rely on Unicode code points and UTF-8/UTF-16 encoding to correctly handle international text and emoji. Debugging floating-point precision bugs requires inspecting the exact IEEE 754 bit pattern behind a number.
How this tool converts between bases, addresses, and floating-point representations
Base-2 (binary), base-8 (octal), base-10 (decimal), and base-16 (hex) all represent the same quantities, just grouped differently.
IPv4 is 32 bits as four 8-bit octets; IPv6 is 128 bits as eight 16-bit hextets written in hex for compactness.
32-bit float gives roughly 7 decimal digits of precision; 64-bit double gives roughly 15–17, at the cost of double the storage.
From choosing a tool tab to exporting your result
Pick Number Converter, IP Address, or IEEE 754 Float depending on what you need to convert or inspect.
Type a decimal, binary, hex, or octal number, an IP address, or a decimal float value into the matching field.
All other bases, the bit visualization, and the IP or float breakdown update instantly as you type.
For the Number Converter, switch between 8, 16, 32, and 64-bit views and toggle signed/unsigned interpretation of bitwise results.
Use the Unicode/ASCII lookup for character encodings, or review the AND/OR/XOR/NOT/shift results for two operands.
Click any result box to copy its value, or use Export Result to download a text summary of the conversion.
Converting decimal 202 to binary, hex, and octal
A developer needs to express the decimal value 202 in binary, hexadecimal, and octal for a low-level debugging task.
Explanation: All three representations — 11001010, CA, and 312 — describe the exact same quantity (202), just grouped differently. Hex is favored in programming because each digit maps cleanly to a 4-bit nibble, making it far more compact and readable than raw binary while still being trivial to convert back.
What each output actually represents
| Output | What It Means | Example |
|---|---|---|
| Binary | The value expressed as base-2 digits (0s and 1s), matching how computers store data | 202 → 11001010 |
| Hexadecimal | A compact base-16 shorthand where each digit represents exactly 4 binary bits | 202 → 0xCA |
| Signed bitwise result | The two's complement interpretation, where the top bit indicates a negative value | ~5 (32-bit) = −6 signed, 4294967290 unsigned |
| IEEE 754 fields | Sign, exponent, and mantissa bits that together encode a decimal value in binary | 1.0 → sign 0, exponent 01111111, mantissa all zeros |
| Subnet mask note | The CIDR prefix length implied by a mask made of consecutive 1-bits then 0-bits | 255.255.255.0 → /24 |
Reading signed vs unsigned: the same raw bit pattern can represent two different decimal numbers depending on interpretation — always confirm which mode (signed or unsigned) is active before comparing bitwise results.
Typical ranges: an 8-bit unsigned value ranges 0–255, 16-bit spans 0–65,535, 32-bit spans roughly 0–4.3 billion, and 64-bit spans up to about 1.8×10¹⁹ — always match the bit width to your actual data type.
Manual verification: to check a hex-to-decimal conversion by hand, multiply each hex digit by 16 raised to its position power and sum the results — e.g. 0xCA = 12×16¹ + 10×16⁰ = 192+10 = 202.
Where number base conversion and bit-level tools are genuinely useful
Practice number systems, bitwise logic, and floating-point representation for CS classes.
Read memory addresses, hex color codes, and debug bit-level flags in application code.
Calculate subnet masks, valid host ranges, and inspect IPv4/IPv6 address structure.
Work with register values, hardware flags, and bit masks in firmware programming.
Inspect binary/hex data structures relevant to hashing, encoding, and encryption routines.
Look up Unicode code points and UTF-8/UTF-16 byte encoding for non-English text and emoji.
Understand why 0.1 + 0.2 ≠ 0.3 exactly by inspecting the IEEE 754 bit pattern behind each value.
Convert hex color codes (#RRGGBB) to and from their decimal RGB components.
Verify IP address ranges and subnet boundaries before deploying infrastructure changes.
Understand floating-point precision limits when working with numeric model weights.
Generate instant conversions and bit visualizations for classroom demonstrations.
Practice binary, hex, and bitwise-operation questions common in technical coding interviews.
Inspect raw byte-level data and address structures when analyzing network traffic or malware samples.
What this binary & hex converter does well, and where it has boundaries
The four number systems this converter translates between
| Base | Digits Used | Bits per Digit | Typical Use |
|---|---|---|---|
| Binary (base 2) | 0–1 | 1 | How computers physically store all data |
| Octal (base 8) | 0–7 | 3 | Legacy Unix file permissions, some older systems |
| Decimal (base 10) | 0–9 | ~3.32 (irrational) | Everyday human-readable numbers |
| Hexadecimal (base 16) | 0–9, A–F | 4 | Memory addresses, color codes, compact binary shorthand |
Summary: This binary & hex converter gives you an instant, free way to convert between number bases, inspect Unicode characters, break down IP addresses, and visualize IEEE 754 floating-point representation — all in one developer-focused tool. Pair it with the Matrix Calculator and Prime Number Checker for a fuller toolkit of math and computer science calculators.
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