Binary translator for text and numbers

Translate text to binary code, and back

Type a word or a sentence and its binary code appears right away: one 8-bit byte per letter, separated by spaces. Paste a string of 0s and 1s instead, and the translator recognizes it and turns it back into text. You can also:

• see each letter’s breakdown, with its code in binary and in decimal;
• copy the result with or without spaces between bytes;
• convert a number between binary, decimal, hexadecimal and octal, with the steps shown;
• do binary math: addition, subtraction, multiplication and division with the remainder.

Binary code works with or without spaces: a long run of 0s and 1s is cut every 8 bits, and a shorter group, like the 7 bits of old ASCII, is padded on the left. It’s free, with no sign-up, and everything runs in your browser.

How text becomes binary code

A computer only stores 0s and 1s, so every character gets a number, and that number is written in binary. Plain English letters, digits and common punctuation follow the ASCII table: capital B is number 66, written 01000010 in one byte. The word “Hello” takes 5 bytes, or 40 bits.

Accented letters, emojis and Chinese characters don’t exist in ASCII. The web uses UTF-8, which keeps the same codes for ASCII characters and adds more than a million others, written in 2 to 4 bytes. The letter é becomes 11000011 10101001, and an emoji takes 4 bytes. The translator uses UTF-8, so binary code from another source reads back correctly.

The alphabet in binary code

Here is every letter in uppercase and lowercase, in one byte each. Lowercase letters differ from uppercase ones by a single bit, the third from the left:

To write your name in binary, put the bytes of its letters side by side, or just type it into the translator, which handles accents too.

Binary to decimal

In binary, each digit is a power of 2 that doubles from one place to the next, starting from the right. To convert, add up the powers of 2 where there’s a 1. In one byte, the places are worth:

So 101101 is 32 + 8 + 4 + 1, which is 45. In the Binary ↔ decimal tab, choose “binary” and type the number: you get the result and the calculation, for up to 64 digits.

Decimal to binary

Divide the number by 2, then divide the quotient by 2, and so on until you reach 0, writing down each remainder. For 45:

1. 45 ÷ 2 = 22, remainder 1
2. 22 ÷ 2 = 11, remainder 0
3. 11 ÷ 2 = 5, remainder 1
4. 5 ÷ 2 = 2, remainder 1
5. 2 ÷ 2 = 1, remainder 0
6. 1 ÷ 2 = 0, remainder 1

Read the remainders from bottom to top: 45 is 101101 in binary. The translator shows these divisions for any number up to 65,535.

Hexadecimal and octal

Binary numbers get long fast. Hexadecimal, or base 16, shortens them: each digit from 0 to 9 and A to F stands for a group of 4 bits. 101101 splits into 0010 1101, which is 2D in hex. It’s the notation for web colors (#FFFFFF for white) and memory addresses. Octal, or base 8, groups bits by 3: 45 is 55 in octal.

Binary math

Binary addition follows the same rules you learned in school, carrying as soon as you reach 2: 0 + 0 = 0, 0 + 1 = 1, and 1 + 1 = 10, which is 0 with a carry of 1. For example, 1011 + 110 = 10001, or 11 + 6 = 17 in decimal. The Binary calculator tab adds, subtracts, multiplies and divides, with the decimal result so you can check.

More free tools

• the Morse code translator writes a message in Morse code and plays it;
• the Roman numeral converter converts numbers and dates;
• Hakim, the AI math tutor, explains a conversion or a calculation step by step.