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

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.

3 - Counting in binary

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

$\begin{array}{cccc} & 0 & 0 & 1 & 1 \\ + & 0 & 1 & 0 & 1 \\ \hline & 1 & 0 & 0 & 0 \\ \end{array}$

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

$\begin{array}{cccc} & & 1 \\ + & & 1 \\ \hline & 1 & 0 \\ \end{array}$ where 1 + 1 = 0 with a carry of 1 and 1 + 0 = 1

Subtraction, multiplication, etc. work this way:

$\begin{array}{cccc} & & \textit{1} & \textit{1} & & \textit{carried digits} \\ \\ & 0 & 0 & 1 & 1 & \\ + & 0 & 1 & 0 & 1 &\\ \hline & 1 & 0 & 0 & 0 & \\ \end{array}$

4 - Translation in

4.1 - Decimal

4.1.1 - 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
…….

4.1.2 - Floating point

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

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.