Bit - Numeral system (Base-2) notation - Binary Number

About

The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1.

Owing to its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used internally by all modern computers.

Counting in binary

It is possible to do arithmetic in base two, e.g. 3+5 is written:

<math> \begin{array}{cccc} & 0 & 0 & 1 & 1 \\ + & 0 & 1 & 0 & 1 \\ \hline & 1 & 0 & 0 & 0 \\ \end{array} </math>

The addition works like normal (base-10) arithmetic, where:

<math> \begin{array}{cccc} & & 1 \\ + & & 1 \\ \hline & 1 & 0 \\ \end{array} </math> where 1 + 1 = 0 with a carry of 1 and 1 + 0 = 1

Subtraction, multiplication, etc. work this way:

<math> \begin{array}{cccc} & & \textit{1} & \textit{1} & & \textit{carried digits} \\ \\ & 0 & 0 & 1 & 1 & \\ + & 0 & 1 & 0 & 1 &\\ \hline & 1 & 0 & 0 & 0 & \\ \end{array} </math>

Translation in

Decimal

Integer

Using Arabic numerals, binary numbers are commonly written using the symbols 0 and 1.

Number Binary coding
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
…….
14 1110
15 1111
…….

Floating point

1.01 in base-2 notation is 1 + 0/2 + 1/4, or 1.25 in decimal notation.

Hexadecimal

Binary Hexadecimal
0 0
1 1
10 2
11 3
100 4
101 5
110 6
111 7
1000 8
1001 9
1010 A
1011 B
1100 C
1101 D
1110 E
1111 F

Hexadecimal is then to easier write. For example, the binary number “100110110100” is “9B4” in hexadecimal.

Documentation / Reference


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