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Binary numeral system

The binary system works with the two numerals 0 and 1. A binary digit is called a bit.

The set of binary numbers is indicated by the symbol B.

 


Explanation

With 1 bit you can make 21 =  2 numbers

0 = 0
1 = 1

With 2 bits you can make 22 = 4 numbers

00 = 0
01 = 1
10 = 2
11 = 3

With 3 bits you can make 23 = 8 numbers

000 = 0
001 = 1
010 = 2
011 = 3
100 = 4
101 = 5
110 = 6
111 = 7

 


Computers

In computers information is stored in bits. With 4 bits you can make 24 = 16 hexadecimal numbers.

0000 =  0
0001 =  1
0010 =  2
0011 =  3
0100 =  4
0101 =  5
0110 =  6
0111 =  7
1000 =  8
1001 =  9
1010 = 10
1011 = 11
1100 = 12
1101 = 13
1110 = 14
1111 = 15

 


Example 1

The 2-adic development of 35 is written as

35 = 1·25 + 0·24 + 0·23 + 0·22 + 1·21 + 1·20 = 1000112

 


Example 2

The calculation 1 + 2 is not allowed, as only 0 and 1 are possible.

 


History

The German mathematician Gottfried Leibniz (1646 - 1716) used binary numbers (bi = two) for many different purposes. For him, 1 stood for God and 0 for nothingness.


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