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