Binary Number System
Today most of the modern computer systems operate using binary logic. The computer represents values using two voltage levels that indicate to either OFF or ON using 0 and 1. For example the voltage 0V is usually represented by logic 0 and either +3.3 V or +5V voltage is represented by logic 1. Thus with two levels we can represent exactly two different values. These could be any two different values, but by convention we use the values 0 and 1.
Since there is a correspondence between the logic levels used by the computer and the two digits used in the binary numbering system, it should come as no surprise that computers employ the binary system.
The binary number system works like the decimal number system except the Binary Number System uses the base 2 and includes only the digits 0 and 1 and use of any other digit would make the number an invalid binary number.
The weighted values for each position are represented as follows:
(Base)power |
27 |
26 |
25 |
24 |
23 |
22 |
21 |
20 |
2-1 |
2-2 |
Value |
128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |
.5 |
.25 |
The following table shows the representation of binary number against the decimal numbers:
Decimal Number |
Binary Number Representation |
0 |
0000 |
1 |
0001 |
2 |
0010 |
3 |
0011 |
4 |
0100 |
5 |
0101 |
6 |
0110 |
7 |
0111 |
8 |
1000 |
9 |
1001 |
10 |
1010 |
11 |
1011 |
12 |
1100 |
13 |
1101 |
14 |
1110 |
15 |
1111 |
Usually in case of decimal numbers, every three decimal digits are separated with a comma to make larger numbers easier to read. For example, it is much easier to read a number 840,349,823 than 840349823.
Getting the inspiration from the same idea, there is a similar convention for binary numbers so that it may be easier to read binary numbers but in case of binary numbers we will add a space every four digits starting from the least significant digit on the left of the decimal point.
For example if the binary value is 1010011001101011, it will be written as 1010 0110 0110 1011.
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