Skip to main content

Introduce the Boolean Algebra

 .

Boolean Algebra

Boolean Algebra is used to analyze and simplify the digital ( logic) circuits. Boolean algebra sometimes referred to as the algebra of logic, is a two valued system of algebra that represents logical relationships and operations. English logician and mathematician George Boole, the first to apply these algebraic techniques to the logic process, contended that any statement (any declarative sentence that is either true or false but not both) could be assigned a binary value, such as "true/false" or "yes/no" or "on/off" of "0/1".
In 1854, Boole wrote An Investigation of the Laws of Thought, in which he discussed ways of reducing logical relationships to simple statements of equality, inequality, inclusion and exclusion. Boole then showed ways to express these statements symbolically, using binary ( two-valued) code, and created algebraic rules that governed these logical relationships.

Truth Table Function

A truth table represents a table having all combinations of inputs and their corresponding result. It is possible to convert the switching equation into a truth table. For example, Consider the following switching equation.
                            F (A,B,C)   =  A+BC
The output will be high (1) if A = 1 or BC = 1 or both are 1. The truth table for this equation is shown by Table (a). The number of rows in the truth table is 2nwhere n is the number of input variables (n=3 for the given equation). Hence there are 23 = 8 possible input combination of inputs.

Truth Table

Boolean Function 

A Boolean function refers to a function having n number of entries or variables, so it has 2n number of possible combinations of the given variables.

Boolean expressions are formed by application of basic operations to one or more Boolean variable or constants. The simplest expression consists of a single constant or variable such as 0, x or x'. A Boolean expression that contains n distinct variables is usually referred to as a Boolean expression of n variables. Each variable or its complement in an expression is referred as literal. 
Boolean expression represents a Boolean function. Substituting 0 and 1 for variable in the expression obtains the value of this function. A truth table specifies the values of a Boolean expression for every possible combination of values of the variables in the expression. 
                            

A

B

B'

F(A,B) = A + B'

0

0

1

1

0

1

0

0

1

0

1

1

1

1

0

1

Table : Truth table of f(A,B) = A + B'

It is to be noted that different Boolean expression may determine the same Boolean function. Two function. For example A.(B + C) and (A.B) + (A.C) determine the same Boolean function. 



Home


Comments

Post a Comment

Popular posts from this blog

Important Questions of Data Structure and Algorithm (DSA)

 . 1. What is Data structure? Explain different operations to be performed on data structure. 2. Define stack as ADT. Convert P+Q-(R*S/T+U) - V*W into infix expression to postfix. 3. Define Queue. Explain its type with example. 4.  Difference between stack and Queue. 5. Difference between Linear Queue and circular Queue. 6. Write an algorithm to enqueue and dequeue data element in a circular queue.                              7. Define Linked List. Explain its type. How does double linked List is different from circular linked   List. 8. What is recursion and recursive function? write a recursive function to compute Fibonacci number. 9. What is an AVL tree ? Create an  AVL tree from the following data:      18, 12, 14, 8, 85, 25, 31, 24, 27 10. Define B-tree? How to insertion and deletions of elements can be done in a B-tree. 11. Create an B-tree from the following Data:  ...
Post a Comment
Read more

Define LAN and WAN

 . Local Area Network (LAN)  A LAN is a network that is used for communicating among computer devices, usually within an office building or home.   LAN’s enable the sharing of resources such as files or hardware devices that may be needed by multiple users • • Is limited in size, typically spanning a few hundred meters, and no more than a mile.  Is fast, with speeds from 10 Mbps to 10 Gbps.  Requires little wiring, typically a single cable connecting to each device.  Has lower cost compared to MAN’s or WAN’s.  LAN’s can be either wired or wireless. Twisted pair, coax or fiber optic cable can be used in wired LAN’s. Advantages of LAN :    The data is transferred at an extremely faster rate in local Area Network.  Local area network (LAN) provides higher security. Disadvantages of LAN :   Initial cost of installing local area network is quite high.  Unauthorized user can access critical data of an organization in case LAN ad...
Post a Comment
Read more

Digital signal and wave form

 . Digital Signal: A digital signal is a representation of information using discrete values, typically in binary code (0's and 1's). They have distinct levels or states, allowing for precise representation of data. Commonly used in digital communication, computers and electronic devices for transmitting and processing information. Digital signals are less susceptible to noise during transmission, making them reliable. Example: Binary-coded messages, digital audio data transmitted over the internet are all examples of digital signals. Digital Waveform: Digital waveform consist of voltage levels that are changing back and forth between the HIGH and LOW level as states. A waveform, on the other hand, is a graphical representation of a signal's amplitude as it varies with time. It shows how the amplitude of the signal changes over a specific period. Waveforms can be associated with both analog and digital signals. It used in signal processing, audio analysis and the study of e...
Post a Comment
Read more