As we know, the most widely used system in the world to represent numbers is the decimal system , also known as base-10, which uses ten digits, from 0 to 9, for all operations carried out with the system. For this system, each space within a number corresponds to a power of 10. A little more technically we could say that the decimal numbering system is a positional type numbering system in which the quantities are symbolized using the powers as an arithmetic base. of the number ten. bolts.answerhop
However, the decimal numbering system is not the only numbering system that exists and that we can implement, since for example we have the so-called binary system, also known as base-2, which uses only the digits 0 and 1. In This type of numbering, each number corresponds to a power of 2. techwadia
This characteristic
makes the binary system the best tool for use in all kinds of
digital operations, and it is the basis of all the technological
devices that we know today, or at least that use digital circuits.
The binary system,
by using only two digits, or binary digits as they are called in this case,
offers only two possible states, "0" or "1". In
this case, the state "0" represents for
example the state "Off" and the
state "1" represents "On". Of
course they do not always represent these states, they may be others.
In this sense, because
binary operations can be carried out with a very simple set of rules, it allows
an infinite number of operations to be carried out just by using a few logic
gates. For example, to multiply two digits together, the only thing we
would need to know is the following rule:
0 x 0 = 0
0 x 1 = 0
1 x 0 = 0
1 x 1 = 1
It should be noted that the
two-value system to represent binary numbers can
also be seen to correspond to the two truth values that are used in symbolic
logic. Consider the following truth tables using the
logical operator "AND:"
F AND F = F
F AND T = F
T AND F = F
T AND T = T
For
example, if we replace "F" by "0" and "T" by "1",
it is clear that the logical operator
"AND" is equivalent to the multiplication sign in the binary
arithmetic system. Of course, all other mathematical
operations can also be exchanged for logical operations.
Since the logical
operators are really easy to represent in the
development of computer circuits, it is possible to build a device that is
capable of carrying out arithmetic operations, the so-called “Boolean
algebra”.