Binary Code

The binary system is a base-2 positional notation system, meaning it's a way of writing numbers using only two digits.

These digits are called bits (for binary digit) and take only the values 0 and 1.

To convert a number $ N $ to binary (format with zeros 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)} $).

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

NB: A number in binary is a sequence of bits in a sequence, where each position has a value which is a power of 2.

Converting text to binary involves associating each character with a number according to a coding table, such as A1Z26 or ASCII. Each number is then converted into binary.

To perform the reverse operation, convert each sequence of bits into a number, then associate that number with the corresponding character in the chosen encoding table.

Converting a binary number involves changing the base from base 2 to base 10. Each bit is multiplied by the power of 2 corresponding to its position.

Binary allows us to represent all numbers. By defining a lookup table between objects (letters, symbols, colors, sounds) and numbers, it becomes possible to encode any information in binary.

The most common encoding in computing is ASCII, where A=65, B=66, etc.

Other encodings exist, such as A1Z26 (A=1, Z=26).

Every digital encoding has a binary representation.

The term binary language is inaccurate. There is no language or formal language called binary language. In computer science, programming languages are translated into machine language, which consists of numerical instructions. These numbers can be represented in binary, which explains the common use of this expression.

Binary code cannot be directly translated: a sequence of bits always represents a number. The meaning depends on the encoding used. For text, tables like ASCII associate a number with a character. An ASCII converter is available on dCode.

A bit (short for binary digit) is the smallest unit of information in computing with two values: 0 or 1.

In computing, memory is finite. Numbers are stored in fixed-size locations, defined by a number of $ N $ bits.

This choice limits the representable values and influences performance and memory consumption.

The number of bits needed depends on the maximum value to be represented. With $ n $ bits, it is possible to encode numbers from $ 0 $ to $ 2^n - 1 $.

Here are the min-max intervals:

For a number written in the form bbbb.bbb, each bit after the decimal point represents a negative power of 2 ($ 2^{-1}, 2^{-2}, \dots $), so use the dCode base-N conversion tool.

For numbers stored according to the IEEE 754 standard, refer to the specific format structure (sign, exponent, mantissa).

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