Divide by N Counter Design

Design of a divide by N counter A divide by N counter counter N number of state following which it resets back to the initial state and starts counting again. For example, a divide by 10  also known as a decade counter counts a total of 10 states from 0 to 9 before resetting to […]

Binary Counter Design

Sequential-Synchronous Counter Design The different steps for the design of the synchronous sequential counter circuits are: i)          State diagram ii)         state table and  excitation table iii)        Simplification using K-Map iv)         Logic Design Number of Flip-Flops required for implementing a counter: For N-bit counter, N flip-flops would be required For counter counting upto  N states, the number […]

Mc-Clusky or Tabulation Method

Introduction In the previous lectures, you have learnt the Boolean algebra and K-Map methods of solving Boolean expressions. These methods are simple and easy for less number of variables say upto four. But for more than 4 variable equations, these become tedious. So, another method known as Quine Mc-Clusky or Tabulation Method is used for […]

Magnitude Comparator

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 […]

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 input […]

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) […]

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