Numbers and Numerals
Introduction to Binary system
The numeral system we usually use has ten digits, from 0 to 9; for this reason, it is known as the base 10 system or the decimal number system. In this system of numeration, we create numbers using the ten digits. For example, 82 and 1024 are decimal numbers. These numbers can also be written as 82(10) and 1024(10).
Another system of numeration is the base 2 system or the binary number system. In this system, we form numbers using the two digits “0” and “1”. For example, 0(2), 1(2), 10(2), 100(2) and 101(2) are binary numbers. These are read as “zero to the base 2”, “one to the base 2”, “one zero to the base 2”, “one zero zero to the base 2” and “one zero one to the base 2”, respectively.
The following table lists a few numbers written as per the base 10 and base 2 systems.
|
Things
|
Unit of Things
|
Decimal Representation
|
Binary Representation
|
|
|
zero |
0 |
0 |
|
* |
one |
1 |
1 |
|
** |
two |
2 |
10 |
|
*** |
three |
3 |
11 |
|
**** |
four |
4 |
100 |
|
***** |
five |
5 |
101 |
|
****** |
six |
6 |
110 |
|
******* |
seven |
7 |
111 |
|
******** |
eight |
8 |
1000 |
|
********* |
nine |
9 |
1001 |
As you can see, binary numbers (above 1) are longer than their decimal equivalents. The bigger a binary number, the longer it i…
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