Binary Numbering System

The decimal system is widely used in everyday life, as it offers us a simpler way to manipulate the numbers in certain mathematical situations, consists of ten numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
The use of Mathematics in different situations does not only concern man, computers use numbers to perform complex calculations with greater speed and practicality. The binary system used by computers is and consists of two digits, 0 and 1. The combination of these digits causes the computer to create various pieces of information: letters, words, texts, calculations.
The creation of the binary numbering system is attributed to the German mathematician Leibniz.
Binary Numbering and Decimal Numbering
Turning Decimal to Binary
14(base10) = 1110(base2)
14 / 2 = 7 remainder 0
7 / 2 = 3 remainder 1
3 / 2 = 1 rest 1
36(base10) = 100100(base2)
36 / 2 = 18 remainder 0
18/2 = 9 remainder 0
9 / 2 = 4 remainder 1
4 / 2 = 2 remainder 0
2 / 2 = 1 rest 0
The binary number will be formed by grouping the last result followed by the remainders of the previous divisions.


turning binary into decimal
110100(base2) = 52 (base10)

1

1

0

1

0

0

house 6

house 5

house 4

house 3

house 2

house 1

25

24

23

22

21

20

1 x 25

1 x 24

0 x 23

1 x 22

0 x 21

0 x 20

1 x 32

1 x 16

0 x 8

1 x 4

0 x 2

0x1

32

16

0

4

0

0


32 + 16 + 0 + 4 + 0 + 0 = 52

1100100(base2) = 100(base10)

1

1

0

0

1

0

0

house 7

house 6

house 5

house 4

house 3

house 2

house 1

26

25

24

23

22

21

20

1 x 26

1 x 25

0 x 24

0 x 23

1 x 22

0 x 21

0 x 20

1 x 64

1 x 32

0 x 16

0 x 8

1 x 4

0 x 2

0x1

64

32

0

0

4

0

0


64 + 32 + 0 + 0 + 4 + 0 +0 = 100

by Mark Noah
Graduated in Mathematics
Brazil School Team

Numerical sets - Math - Brazil School

Source: Brazil School - https://brasilescola.uol.com.br/matematica/sistema-numeracao-binaria.htm

Queen's Carpet: Learn more about the plant that conquered Brazilians

Queen's Carpet: Learn more about the plant that conquered Brazilians

Firstly, the Queen's Carpet is of the Episcia Cupreata species, which is a type of vine and has i...

read more

Do you know about purchase protection for credit cards?

Some cards may offer this advantage through annual fees, with amounts that vary from bank to bank...

read more

Apple is again the most valuable company in the world; check the top 10

According to a study by Kantar Brandz, the technology company apple once again became the most va...

read more