Magnitude Comparator: A magnitude comparator is a combinational circuit that compares two binary numbers and determines their relative magnitude. The schematic block diagram in figure-1 has two inputs and three outputs. It compares two numbers for equality, less than and greater than conditions. Depending on the comparison, one of the output will be true and […]

### Category: STLD/Digital Electronics

## Decoder and Encoder

Implementing with Decoders: A decoder is a combinational circuit that converts N-bit binary information to 2N unique output lines. It is able to represent upto 2N distinct elements of coded information. General type decoders usually come in sizes of Nx2N where N is the number of input lines. With a given input, only one of […]

## Multiplexers and De-Multiplexers

Introduction to Multiplexer: A multiplexer also called as a data selector, is a combinational circuit used to select information from one of the many input sources and directs it to a single output line. A multiplexer has several data input lines but only one output. Control or selection lines are used for selecting one of the […]

## Adder Circuits

Adder Circuits An adder is a combinational circuit that adds multi-bit (two or more). Different types of adders are: Half Adder : A combinational circuit that adds 2-bits Full Adder : A combinational circuit that adds 2-bits and a carry from the previous stage of addition. Ripple Carry Adder/ or Carry Propagate Adder: An adder that add […]

## Introduction to Karnaugh-Map

Karnaugh Map (K-map) K-Map is a pictorial representation of the Boolean function. It is a systematic method of simplifying the Boolean expression. A K-Map is an arrangement of the adjacent cell , each cell representing the minterm or the maxterm of the SOP or the POS equations. The number of adjacent cells in a K-Map […]

## Boolean Function

Boolean Functions The following steps are generally followed while designing the logic circuits using Boolean functions. Analysis of the given statement of the problem to find the number of variables Writing the truth table from the given statement Conversion of the truth table into a logic function/ Boolean expression using standard product of sums(SOP) or […]

## Boolean Theorems

Duality Principle: Dual of an expression can be obtained by : Changing all + with . Complement 0’s and 1’s i.e. 1’=0 and 0’=1 Keep the variable sam (i.e. do not complement the variable) Example: Find the dual of : A(B+C) = AB + AC Solution: Find the Dual of F(xyz)=(x+y) (x+z)(y+z) Solution: (x+y) […]

## Axioms and Laws of Boolean Algebra

Boolean Algebra Axioms and Laws of Boolean Algebra Boolean algebra devised in 1864 by George Boole, is a system of mathematical logic. It is an algebraic system consisting of a set of element (0,1) associated with a Boolean variable and two binary operators AND and OR and a uniry operator NOT. In mathematics, an identity is a […]

## Hamming Code

Hamming Code Hamming code is an improvement over the other parity systems, this approach enable us to detect one bit error that might get introduced during transmission in every byte of information, However, this is done at the cost of increased data size due to introduction of multiple parity bits. Calculating the Hamming Code […]

## Parity Code

Error Detecting Codes: When we transmit a computer code over a medium, the possibility of a bit being lost due to transient or any other reason become the point of interest. During data sharing, the flow of information on the channel require high data integrity for the system to properly work on that data. So, […]