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
2^5	2^4	2^3	2^2	2^1	2^0
1 x 2^5	1 x 2^4	0 x 2^3	1 x 2^2	0 x 2^1	0 x 2^0
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
2^6	2^5	2^4	2^3	2^2	2^1	2^0
1 x 2^6	1 x 2^5	0 x 2^4	0 x 2^3	1 x 2^2	0 x 2^1	0 x 2^0
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