What is Binary?
adj. Composed of two elements, units or figures.
Crist. binary axis of the axis of symmetry of a crystal when giving the crystal a complete turn on it takes two equal positions.
electron. Numbering code in base two, used in the processing of information by means of electrical signals. The only two values it can take are 0 and 1.
inform. Method of memorizing and manipulating numbers and characters based on two states: 0 and 1. A 0 represents the off state (deactivated) and a 1 indicates the on (activated) state.
mat. Numbering system in which a number is represented by a succession of two unique symbols.
In Mathematics it is a numbering system by which a certain number is represented by a succession of two unique symbols.
As in the decimal system, numbers can be placed to the left or right of the decimal point, in the binary system:
The number to the left of the point is an integer called units. Going to the left each position is worth 2 times more.
The first figure to the right of the point means halves. When going to the right, each position is worth 2 times less, or half of the previous one.
Examples of some numbers:
In the decimal system 1 equals 1 in binary
In the decimal system, 2 equals 10
El, 3, to 11; 4 to 100; 9 to 1001 etc.
Both in Computer science and in telecommunications, this code is used with different data coding methods such as character or bit strings. These methods can be of a variable or fixed width. In a fixed width one, for example, each digit or letter is represented by a string of bits of equal length, such as a binary number found in tables with decimal, hexadecimal or octal notation.
For Electronics it is a code numbering in base two, which is used in the treatment of information by electrical signals. The two unique values that are taken are 0 and 1.
On the other hand, in Crystallography the axis of symmetry of a crystal is called the binary axis when the crystal takes a complete turn on it takes two equal positions.
How to form a binary number?
Given a number, the method consists of a sequence of “integer divisions” until it reaches zero. From here we will take note of the rest of each division, thus forming our binary number. Let’s proceed with an example, considering number 27 again.
Div 1: 27/2 = 13 with remainder 1 Div 2: 13/2 = 6 with remainder 1 Div 3: 6/2 = 3 with remainder 0 Div 4: 3/2 = 1 with 1 Div remainder 5: 1/2 = 0 with remainder 1.
Once the divisions have been completed, it is sufficient to recompose the remains starting from the bottom up, thus obtaining the corresponding binary number.
Then, proceeding from the rest of div 5, then div 4 and so on we will get 11011. Exactly the binary number relative to the decimal number 27.
Let’s see the steps to know how to go from binary to decimal.
First of all, given a binary number, we need to take one digit at a time and multiply it by (2 ^ x) where x corresponds to the position of the digit. Seeing the example, it will be easier to understand how to do it.
We can do the binary number 100111 in its decimal number, doing the following calculation:
1 x 2 5 + 0 x 2 4 + 0 x 2 3 + 1 x 2 2 + 1 x 2 1 + 1 x 2 0 =
= 1 x 32 + 0 x 16 + 0 x 8 + 1 x 4+ 1 x 2 + 1 x 1 =
= 32 + 0 + 0 +4 +2 + 1 = 39.
As a result, 39 represents the equivalent number of the decimal system.
Then we can say the following:
100111 (2) = 39 (10).
Another example is to take 27 whose representation in base 2 is 11011, because we do the following:1 * (2 ^ 4) + 1 * (2 ^ 3) + 0 * (2 ^ 2) + 1 * (2 ^ 1) + 1 * (2 * 0) = 16 + 8 + 0 + 2 + 1 = 27.