What is Boolean algebra? And logic gates?

What is Boolean algebra?  And logic gates?

Boolean Algebra

Introduction:

Boolean algebra is algebraic structures that are closely connected to some other branches such as that are called group theory and linear algebra. There are many mathematicians remain on trying to solve the logical problems using conventional algebra and George Boole, a great mathematicians successfully come at a solution with its on mathematical system of logic. We explained the Boolean algebra in this blog “An investigation of the laws of thought” and Boolean algebra behind on it was called as switching Algebra.  

 « Meaning:

Boolean algebra is a system of algebra and that is based on only the two values 0 and 1. Binary logic distribute with variables that can take only two discrete values. The two values lay hold of by variables can be true or false, and yes or no, and 0 or 1. The computer can understand only the binary signals that are in form of on/off, true/false or 0/1. Consequently, Boolean algebra is defined as a set of elements, put of postulates and place of operations to be performed on the elements. A put of elements is any collection of objects that having a common property. The operations carry out in Boolean algebra are called as the logical operations. These type of logical operations are called AND, OR, NOT and these operations can be execute with the help of Logic gates.

Logical operations

AND	.	(x.y)
OR	+	(x+y)
NOT	‘	x’

 «  Logical operations
Boolean algebra used to helps in solving complex/compound expressions. To execute the compound statement or logical functions, and logical operators like AND, OR and NOT are will be used. These particular logical operators are also used to combine logical variables and the constants to from logical expressions. This type of logical operator is used to perform the logical operations. Thus logical operations can be executed with the help of Logic gates. 

i)                    AND operations: AND operation is used to merge two different variables and it is constituted by dot (.). Example: x.y or A.B, X.Y and it will be read as X and Y. Rules of AND operations are:

Truth table of And operations:

X.Y	Z
T.T	T
T.F	F
F.F	F
F.T	F

X	Y	X.Y
1	1	1
1	0	0
0	1	0
0	0	0

     

i)                    OR operations: Once A and B are combined by use of OR operator to acquire result, then it is called OR operation is constitute by plus (+) sign. Example X+Y always read as X OR Y.

Rules of OR operation:

1 + 1 = 1

1 + 0 = 1

0 + 1 = 1

0 + 0 = 0

Truth table of OR operation:

           

X	Y	X+Y
1	1	1
1	0	1
0	1	1
0	0	0

    

ii)                  NOT operation: NOT operation works on a single variable and operation execute by NOT is called complement. NOT operation is constitute by a prime or bar i.e. (‘) or (-) over variables. Example X’ means that complement of X.

Truth table of NOT operation:

Input (X)	Output (X’)
1	0
0	1

X’ will be always read as NOT X or the complement of X.

« Applications of Boolean Algebra:

1.      Boolean algebra is executing to non-numerical problems like psychiatry.

2.      Boolean algebra is also used in electronic devices like digital computers, pocket calculators, cellular phones on that rules of Boolean algebra applied.

3.      Boolean algebra used in many spheres of occupation like telecommunication and Electronics Engineering controlling the pulse flow/current flow.

4.      It is used in circuit designs, in the field of digital engineering where 0 and 1 constitute the two different states in a digital circuit i.e. 1 for the high voltage and 0 for the low voltage.

5.      It can also help to performing queries that involves use of Boolean logic i.e. where needs to be satisfy.

Logic gates:

In computers, all the instructions and data are constituted as electrical signals or current. Electrical signals run internally just like the electronic switches that can be either in open or closed state. And a bit level, existing of current is constituted in binary form i.e. 1 or 0 where 1 means to ‘Open’ and ‘0’ means to close.

«  Meaning: Logical gates are graphical constitute of electronic circuits that works as one or more signals given as input so that output can be build. In other words, ‘Logic gates’ are such digital IC’s of which  output is set on by their different states that are given as input and this state can be the form of 0 and 1 or True/False. These all logic gates are mostly used to design circuits.

Different Logic gates are used to execute logical operations like:

AND, OR, NOT, XOR, NOR and so on.

 ·         AND gate: AND gate is used to run the logical operation AND that can produce high output 1 when all the inputs are high i.e. 1. AND gate can be provide two or more signals as input but produces only the one signal as output.

Example: x.y = x AND y.

 ·         OR gate: ‘OR’ gate is used to run the logical operation OR that produces high output 1 in all combinations of the input excluding if all inputs are 0.

Example: x+y = x OR y.

 ·         NOT gate: NOT gate is used to perform the logical operation NOT that which produces the invert output of the input signals. (‘) that symbol is used for the NOT operation.

 ·         NOR gate: NOR gate is an inverted OR gate and it is also called as Bubbled OR gate. This type of gates two inputs are given and only one output is produced.