Binary Converter

Translate text to binary, convert number systems with step-by-step math steps, and toggle bits on an interactive bitboard.

Binary Converter & Translator

Translate English text into binary code, convert numbers between bases (binary, decimal, hexadecimal, octal) with step-by-step calculation walkthroughs, or toggle individual bits using our interactive grid board.

Plain Text (ASCII/UTF-8)

Binary Code

Translation Formatting

Number Registers

Step-by-Step Math Walkthrough

Enter a number in any register to inspect the step-by-step conversion steps dynamically.

Clickable Registers

Bit Board Value Translation

Binary Value00000000
Decimal Value0
Hex Value0x00
ASCII Symbol[NUL]

What is the Binary Number System?

The Binary Number System is a base-2 positional notation system that uses only two symbols: 0 (zero) and 1 (one). In computer science and digital electronics, these binary digits are called bits.

Unlike the decimal system (base-10), which uses ten digits (0-9) and increments in powers of ten, the binary system increments in powers of two. Each position in a binary number represents a specific power of 2, starting with $2^0$ on the far right (least significant bit) and increasing to the left.

Positional Weights in a Byte (8 Bits)

A group of 8 bits is called a byte. The positional values (weights) of a byte from left to right are:

Position Index 7 6 5 4 3 2 1 0
Power of 2 $2^7$ $2^6$ $2^5$ $2^4$ $2^3$ $2^2$ $2^1$ $2^0$
Decimal Weight 128 64 32 16 8 4 2 1

For example, the binary string 01001101 represents: $$(0 \times 128) + (1 \times 64) + (0 \times 32) + (0 \times 16) + (1 \times 8) + (1 \times 4) + (0 \times 2) + (1 \times 1) = 64 + 8 + 4 + 1 = 77$$

Step-by-Step Number Base Conversions

Converting numbers between bases is a fundamental programming skill. Our tool computes these conversions instantly and displays the mathematical steps:

1. Converting Decimal to Binary (The Division-by-2 Method)

To convert a decimal integer to binary, repeatedly divide the number by 2 and write down the remainder. Continue until the quotient is 0. Reading the remainders from bottom to top (most significant bit to least significant bit) gives the binary value.

Example: Convert Decimal 13 to Binary:

  1. $13 \div 2 = 6$ with remainder 1
  2. $6 \div 2 = 3$ with remainder 0
  3. $3 \div 2 = 1$ with remainder 1
  4. $1 \div 2 = 0$ with remainder 1

Reading the remainders from bottom to top yields 1101.

2. Converting Binary to Decimal (The Power Method)

Multiply each bit by its corresponding power of 2 and sum the results.

Example: Convert Binary 1011 to Decimal:

  • $1 \times 2^3 = 8$
  • $0 \times 2^2 = 0$
  • $1 \times 2^1 = 2$
  • $1 \times 2^0 = 1$
  • Total: $8 + 0 + 2 + 1 = 11$

Translating Text to Binary (ASCII / UTF-8)

When you write letters, numbers, or punctuation, computers store these characters as numbers using character encoding systems. The most common standard for English text is ASCII (American Standard Code for Information Interchange), which has been extended by UTF-8 to support global symbols and emojis.

How Text Translation Works:

  1. Each character in your text is mapped to its integer character code (e.g., 'H' = 72, 'e' = 101).
  2. The decimal character code is converted into an 8-bit binary byte:
    • 72 = 01001000
    • 101 = 01100101
  3. The resulting binary bytes are joined together, usually separated by a space for readability.

Hexadecimal, Octal, and Binary Relationships

Programmers often use Hexadecimal (base-16) and Octal (base-8) as shorter ways to represent binary values:

  • Hexadecimal (Base-16): Uses digits 0-9 and letters A-F. A single hex digit represents exactly 4 binary bits (a “nibble”). For example, binary 1111 is F in hex, and binary 1010 is A. This makes hex very convenient for representing bytes (e.g., binary 10101111 is hex AF).
  • Octal (Base-8): Uses digits 0-7. A single octal digit represents exactly 3 binary bits.

Our tool allows you to type into any base field (Decimal, Binary, Hex, or Octal) and will dynamically sync all other base values in real-time.

100% Client-Side Processing

DwellixTools prioritizes your security. All calculations, translations, and bitboards in this tool run entirely inside your browser using local JavaScript. No inputs, text messages, or numeric values are sent to our server, keeping your data private.