What is a Binary number?

In mathematics and digital electronics, a binary number is lots expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically “0” (zero) and “1” (one).

The base-2 numeral system is a positional notation with a radix of 2. Each digit is known as a bit. Due to its straightforward execution in digital electronic circuitry using logic gates, the binary system can be used by virtually all modern computers and computer-based devices.

Source: online text to binary conversion

Representation

Any number could be represented by a sequence of bits (binary digits), which could be represented by any mechanism with the capacity of being in two mutually exclusive states. The pursuing rows of symbols could be interpreted as the binary numeric value of 667:

1010011011

|―|――||―||

☒☐☒☐☐☒☒☐☒☒

ynynnyynyy

The numeric value represented in each case depends upon the worthiness assigned to each symbol. In the last days of computing, switches, punched holes and punched paper tapes were used to represent binary values.[30] In today’s computer, the numeric values could be represented by two different voltages; on a magnetic disk, magnetic polarities can be utilized. A “positive”, “yes”, or “on” state isn’t necessarily equal to the numerical value of 1; this will depend on the architecture used.

Commensurate with customary representation of numerals using Arabic numerals, binary numbers are generally written using the symbols 0 and 1. When written, binary numerals are often subscripted, prefixed or suffixed to be able to indicate their base, or radix. The following notations are equivalent:

  • 100101 binary (explicit statement of format)
  • 100101b (a suffix indicating binary format; also called Intel convention[31][32])
  • 100101B (a suffix indicating binary format)
  • bin 100101 (a prefix indicating binary format)
  • 1001012 (a subscript indicating base-2 (binary) notation)
  • %100101 (a prefix indicating binary format; also referred to as Motorola convention[31][32])
  • 0b100101 (a prefix indicating binary format, common in programming languages)
  • 6b100101 (a prefix indicating number of bits in binary format, common in programming languages)

When spoken, binary numerals are often read digit-by-digit, to be able to distinguish them from decimal numerals. For instance, the binary numeral 100 is pronounced one zero, instead of a hundred, to make its binary nature explicit, and for purposes of correctness. Since the binary numeral 100 represents the value four, it might be confusing to refer to the numeral as one hundred (a word that represents a completely different value, or amount). Alternatively, the binary numeral 100 can be read out as “four” (the correct value), but this does not make its binary nature explicit.

Conversion to and from other numeral systems

Decimal

To convert from a base-10 integer to its base-2 (binary) equivalent, the quantity is divided by two. The rest is the least-significant little bit. The quotient is usually again divided by two; its remainder becomes another least significant bit. This technique repeats until a quotient of 1 is reached. The sequence of remainders (like the final quotient of 1) forms the binary value, as each remainder should be either zero or one when dividing by two. For instance, (357)10 is expressed as (101100101)2.[34]

Conversion from base-2 to base-10 simply inverts the preceding algorithm. The items of the binary number are used one at a time, starting with the most important (leftmost) bit. You start with the value 0, the last value is doubled, and another bit is then put into produce another value. This is organized in a multi-column table. For instance, to convert 100101011012 to decimal: