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Binary Code

Tool to make binary conversions. Binary code is a numeric system using base 2 used in informatics, symbols used in binary notation are generally zero and one (0 and 1).

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Binary Code -

Tag(s) : Arithmetics, Character Encoding, Substitution Cipher

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# Binary Code

## Binary to Numbers Converter

 Display The binary number and its decimal representation in base 10 Only the base 10 decimal results

## Binary to Text (ASCII) Converter

The binary is often used to encode text in ASCII, use the dedicated page to translate binary into text:

⮞ Go to: ASCII Code

## Binary Converter/Encoder

### How to convert a number in binary?

To convert a number $N$ to binary (format with zeroes and ones) consists in an arithmetic base conversion from base 10 (decimal base noted $N_{10}$) to base 2 (natural binary code noted $N_{2}$).

Example: $5_{10} = 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 101_{2}$

The method consists in making successive divisions by $2$ and noting the remainder ($0$ or $1$) in the reverse order.

Example: With the number 6: $6/2 = 3$ remains $0$, then $3/2 = 1$ remains $1$, then $1/2 = 0$ remains $1$. The successive remainders are $0,1,1$ so $6_{10}$ is written $110_{2}$ in binary.

### How to convert a text in binary?

Associate with each letter of the alphabet a number, for example by using the A1Z26 code or the ASCII code. This will replace each letter by a number that can then be converted to binary (see above).

Example: AZ is 65,90 (ASCII code) so 1000001,1011010 in binary

Similarly for binary to text translation, convert the binary to a number and then associate that number with a letter in the desired code.

### How to convert from binary

It is a base conversion from base 2 to base 10

Example: 111 (base 2) = 1*2^2+1*2^1+1*2^0 = 7 (base 10)

### How to translate binary

The binary does not directly translate, any number encoded in binary remains a number. On the other hand, it is common in computer science to use binary to store text, for example by using the ASCII table, which associates a number with a letter. An ASCII translator is available on dCode.

### What is a bit?

A bit (contraction of binary digit) is a symbol in the binary notation: 0 or 1.

### Why defining a number of bits?

In computer informatics, size is limited, numbers are stocked in memory cells of size N where N is the number of bits.

### how many bits are necessary to represent a number?

This depends on the size of the number, here are the min-max intervals:

 0-1 1 2-3 2 4-7 3 8-15 4 16-31 5 32-63 6 64-127 7 128-255 8 256-511 9 512-1023 10 1024-2047 11 2048-4095 12 2^(n-1) - (2^n)-1 n

### What is 1's complement?

In informatics, one's complement is writing a number negatively inversing 0 and 1.

Example: 0111 becomes 1000, so 7 becomes -7

### What is 2's complement?

In informatics, one's complement is writing a number negatively inversing 0 and 1 and adding 1.

Example: 0111 becomes 1001

### Why is there 10 kinds of people in the world?

There are 10 kinds of people in the world, those that understand binary, and those that don't...

10 in binary equals 2 in decimal.

## Source code

dCode retains ownership of the online "Binary Code" source code. Except explicit open source licence (indicated CC / Creative Commons / free), the "Binary Code" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Binary Code" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, copy-paste, or API access for "Binary Code" are not public, same for offline use on PC, tablet, iPhone or Android ! Remainder : dCode is free to use.

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