Binary Base 2

Digits: 0, 1 only

Decimal Base 10

Digits: 0–9

Hexadecimal Base 16

Digits: 0–9, A–F

Octal Base 8

Digits: 0–7

ASCII Text ASCII

Any printable character

Base 32 Base 32

Digits: A–Z, 2–7

PRESETS:

🔢 Bit Visualizer (click to toggle) —

🧮 Step-by-Step Conversion

📜 Conversion History

📊 Number Properties

Decimal Value—

Bit Length—

Byte Size—

Set Bits (1s)—

Clear Bits (0s)—

Is Power of 2—

Is Even/Odd—

Highest Set Bit—

Hex Representation—

Signed 8-bit—

Signed 16-bit—

📖 Quick Reference

10 = 1010Decimal 10 in binarybin

255 = FFMax 8-bit unsignedhex

128 = 10000000MSB of a bytebin

65535 = FFFFMax 16-bit unsignedhex

41 = 'A'ASCII letter Aascii

0 = NULLASCII null charctrl

32 = SpaceASCII space charascii

127 = 1111111Max 7-bit / DELbin

INT_MAXMax 32-bit signed intdec

0x1 = 00000001Least significant bitbit

Why Use KJSynthora Binary Converter?

🔢

All Number Bases

Instantly convert between binary, decimal, hexadecimal, octal, base-32 and ASCII simultaneously.

⚙️

Bitwise Calculator

AND, OR, XOR, NOT, NAND, NOR, XNOR, left/right shift, unsigned right shift with full binary display.

📐

IEEE 754 Float

Convert decimal floats to 32-bit and 64-bit IEEE 754 representation with sign, exponent and mantissa breakdown.

🔄

Two's Complement

Convert signed integers in 8, 16 or 32-bit two's complement format used in all modern CPUs.

📊

Bit Visualizer

Interactive bit grid — click any bit to toggle it. Shift, rotate, invert, set all bits visually.

🧮

Step-by-Step

See the full division/remainder breakdown of each conversion — perfect for students learning number systems.

📜

Gray Code & BCD

Convert decimal to Gray code and BCD (Binary Coded Decimal) used in digital electronics and displays.

🔤

ASCII Table

Full 128-character ASCII reference with binary, hex, octal and decimal values. Click any row to use.

Binary & Number Systems Guides

Tutorial

Binary to Decimal: Step-by-Step Conversion Guide with Examples

Learn how to manually convert binary to decimal using positional notation, with 15 worked examples from simple to complex.

KJSynthora Team·6 min read·CS Fundamentals

Programming

Bitwise Operators in C, Java & Python — A Complete Reference

AND, OR, XOR, NOT, shift operators explained with real code examples, common patterns, and performance tips.

KJSynthora Team·8 min read·Low-level

Deep Dive

IEEE 754 Floating Point: Why 0.1 + 0.2 ≠ 0.3 in Every Language

A visual explanation of how floats are stored in memory, why precision errors occur, and how to handle them in your code.

KJSynthora Team·9 min read·Computer Science

Frequently Asked Questions

How do I convert binary to decimal? +

Multiply each bit by its positional value (a power of 2) and sum them. Starting from the right, bit positions are 2⁰=1, 2¹=2, 2²=4, 2³=8, etc. Example: 1011 = 1×8 + 0×4 + 1×2 + 1×1 = 11. Our tool shows you this step-by-step breakdown in the Converter tab.

What is two's complement and why is it used? +

Two's complement is the most common method for representing signed (positive and negative) integers in binary. To get the two's complement of a number: invert all bits (one's complement) then add 1. This method allows the same hardware adder to handle both addition and subtraction, which is why all modern CPUs use it. An 8-bit two's complement can represent -128 to +127.

What are bitwise operators used for in programming? +

Bitwise operators work directly on binary representations of integers. Common uses: AND (&) for masking/checking flags, OR (|) for setting flags, XOR (^) for toggling bits or simple encryption, NOT (~) for inverting, left shift (<<) for fast multiplication by powers of 2, right shift (>>) for division. They're heavily used in low-level programming, cryptography, compression algorithms, graphics, and embedded systems.

What is IEEE 754 and how does floating point work? +

IEEE 754 is the standard for representing floating-point numbers in binary. A 32-bit float has 3 parts: 1 sign bit (positive/negative), 8 exponent bits (the magnitude), and 23 mantissa bits (the significant digits). The value is: (-1)^sign × 2^(exponent-127) × (1.mantissa). This is why 0.1 cannot be exactly represented — just like 1/3 can't be exactly written in decimal. Our IEEE 754 tab shows you the exact binary layout.

What is Gray code and when is it used? +

Gray code (also called reflected binary) is a binary sequence where adjacent numbers differ by only one bit. This prevents multiple bit changes during transitions, which can cause errors in hardware. It's used in rotary encoders (measuring rotation angle), error correction, Karnaugh maps in digital logic design, and analog-to-digital converters.

What is the difference between signed and unsigned binary? +

Unsigned binary uses all bits to represent positive values (0 to 2ⁿ-1). Signed binary reserves the most significant bit (MSB) to indicate sign, with the remaining bits representing the magnitude using two's complement. An 8-bit unsigned integer ranges 0–255; an 8-bit signed integer ranges -128 to +127. The bit pattern 11111111 means 255 (unsigned) or -1 (signed two's complement).

Binary Converter