What is 21 in binary
The binary system
What is the binary system?
We usually use numbers made up of the digits 09. After the 9, when "counting up" this digit comes back to 0 and the next higher digit is incremented by one. For example, after the number 3019 comes the number 3020. On the ones digit, the 9 became a 0, and on the tens digit, the 1 became a 2.
After the 1999 comes the 2000: Here the change continues, so to speak, from the ones digit to the thousands digit.
Since a new digit is started from 10 and every tenfold (100, 1000 ...), our number system is called the system of ten or Decimal system.
in the Binary system there are only the digits 0 and 1. After the 1 comes the 0 again, and at the same time the next digit is incremented by one. After the 10000 (read: "onezerozerozerozero", not "ten thousand") comes the 10001 and then the 10010. The 1 in the last digit has become the zero, and the 0 has been changed to the second digit from the right the 1.
Here, too, they may propagate these changes over many places, which even happens very often: For example, 1101010000 comes after 1101001111.
The result is the following series of binary numbers: 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, 10000, 10001 ...
When "juxtaposing" the numbers of the decimal system and the binary system that belong together, one discovers different rules:
Decimal  Binary system  Observations:
At the Converting numbers from the binary system to the decimal system it is checked in places whether there is a 1 on the spot (e.g. on the four digit). If so, the value of the digit (in the example: 4) is added. Example: 1011011_{2} The ones sit on the ones, the two, the eight, the sixteen and the 64 digits. (See also the first example in the table) 64 + 16 + 8 + 2 + 1 = 91 Therefore: 1011011_{2} = 91_{10} At the Convert from decimal to binary if you proceed in reverse: Examples:
The best way to do this is:


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