Q. Can you explain Binary Number Systems?
The Binary numbers are used to represent digital information because like most digital systems, binary numbers have only two possible states. Ever since the majority of digital systems use only two states to represent data (0V for off & 5V for on) a numbering system that contains only two digits matches perfectly.
The Most modern computer systems (including the IBM PC) operate using binary logic. The computer represents values using two voltage levels (usually 0V for logic 0 and either +3.3 V or +5V for logic 1) and with two levels we can represent exactly two different values and these could be any two different values, but by convention we use the values zero and one as well These two values, coincidentally, correspond to the two digits used by the binary number system.
Ever 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 and the binary number system works like the decimal number system except the Binary Number System:
- uses base 2
- includes only the digits 0 and 1 (any other digit would make the number an invalid binary number)
The weighted values for each position are determined as follows:
|
2^7
|
2^6
|
2^5
|
2^4
|
2^3
|
2^2
|
2^1
|
2^0
|
2^-1
|
2^-2
|
|
128
|
64
|
32
|
16
|
8
|
4
|
2
|
1
|
.5
|
.25
|
To make binary numbers completely readable, we will add a space every four digits starting from the least significant digit on the left of the decimal point. For illustration, the binary value 1010111110110010 will be written 1010 1111 1011 0010.